2
0
mirror of https://github.com/boostorg/math.git synced 2026-01-19 04:22:09 +00:00

Rebuild math documentation.

[SVN r63507]
This commit is contained in:
Daniel James
2010-07-01 22:22:00 +00:00
parent 999f37a21e
commit 3f86e4ba70
307 changed files with 18099 additions and 21005 deletions

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@@ -1,10 +1,10 @@
<html>
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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@@ -20,11 +20,11 @@
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<div class="toc"><dl>
@@ -53,7 +53,7 @@
</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 © 2005 John Maddock<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<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>
@@ -61,7 +61,7 @@
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<hr>
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@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>acos</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<link rel="prev" href="asin.html" title="asin">
<link rel="next" href="atan.html" title="atan">
@@ -20,22 +20,22 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="asin.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inverse_complex.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="atan.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="complex_number_tr1_algorithms.inverse_complex.acos"></a><a href="acos.html" title="acos">
<a name="complex_number_tr1_algorithms.inverse_complex.acos"></a><a class="link" href="acos.html" title="acos">
acos</a>
</h3></div></div></div>
<a name="complex_number_tr1_algorithms.inverse_complex.acos.header_"></a><h5>
<a name="id447567"></a>
<a href="acos.html#complex_number_tr1_algorithms.inverse_complex.acos.header_">Header:</a>
<a name="id760032"></a>
<a class="link" href="acos.html#complex_number_tr1_algorithms.inverse_complex.acos.header_">Header:</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">complex</span><span class="special">/</span><span class="identifier">acos</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<a name="complex_number_tr1_algorithms.inverse_complex.acos.synopsis_"></a><h5>
<a name="id447660"></a>
<a href="acos.html#complex_number_tr1_algorithms.inverse_complex.acos.synopsis_">Synopsis:</a>
<a name="id760104"></a>
<a class="link" href="acos.html#complex_number_tr1_algorithms.inverse_complex.acos.synopsis_">Synopsis:</a>
</h5>
<pre class="programlisting"><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>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">acos</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">z</span><span class="special">);</span>
@@ -50,7 +50,7 @@
</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 © 2005 John Maddock<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<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>
@@ -58,7 +58,7 @@
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<hr>
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@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>acosh</title>
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
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<link rel="prev" href="asinh.html" title="asinh">
<link rel="next" href="atanh.html" title="atanh">
@@ -20,22 +20,22 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="asinh.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inverse_complex.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="atanh.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="complex_number_tr1_algorithms.inverse_complex.acosh"></a><a href="acosh.html" title="acosh">
<a name="complex_number_tr1_algorithms.inverse_complex.acosh"></a><a class="link" href="acosh.html" title="acosh">
acosh</a>
</h3></div></div></div>
<a name="complex_number_tr1_algorithms.inverse_complex.acosh.header_"></a><h5>
<a name="id499993"></a>
<a href="acosh.html#complex_number_tr1_algorithms.inverse_complex.acosh.header_">Header:</a>
<a name="id760740"></a>
<a class="link" href="acosh.html#complex_number_tr1_algorithms.inverse_complex.acosh.header_">Header:</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">complex</span><span class="special">/</span><span class="identifier">acosh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<a name="complex_number_tr1_algorithms.inverse_complex.acosh.synopsis_"></a><h5>
<a name="id500086"></a>
<a href="acosh.html#complex_number_tr1_algorithms.inverse_complex.acosh.synopsis_">Synopsis:</a>
<a name="id760813"></a>
<a class="link" href="acosh.html#complex_number_tr1_algorithms.inverse_complex.acosh.synopsis_">Synopsis:</a>
</h5>
<pre class="programlisting"><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>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">acosh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">z</span><span class="special">);</span>
@@ -50,7 +50,7 @@
</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 © 2005 John Maddock<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<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>
@@ -58,7 +58,7 @@
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<hr>
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<a accesskey="p" href="asinh.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inverse_complex.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="atanh.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>asin</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" href="../../index.html" title="Complex Number TR1 Algorithms">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Complex Number TR1 Algorithms">
<link rel="up" href="../inverse_complex.html" title="Complex Number Inverse Trigonometric Functions">
<link rel="prev" href="implementation.html" title="Implementation and Accuracy">
<link rel="next" href="acos.html" title="acos">
@@ -20,22 +20,22 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="implementation.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inverse_complex.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="acos.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="complex_number_tr1_algorithms.inverse_complex.asin"></a><a href="asin.html" title="asin">
<a name="complex_number_tr1_algorithms.inverse_complex.asin"></a><a class="link" href="asin.html" title="asin">
asin</a>
</h3></div></div></div>
<a name="complex_number_tr1_algorithms.inverse_complex.asin.header_"></a><h5>
<a name="id447439"></a>
<a href="asin.html#complex_number_tr1_algorithms.inverse_complex.asin.header_">Header:</a>
<a name="id759795"></a>
<a class="link" href="asin.html#complex_number_tr1_algorithms.inverse_complex.asin.header_">Header:</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">complex</span><span class="special">/</span><span class="identifier">asin</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<a name="complex_number_tr1_algorithms.inverse_complex.asin.synopsis_"></a><h5>
<a name="id446168"></a>
<a href="asin.html#complex_number_tr1_algorithms.inverse_complex.asin.synopsis_">Synopsis:</a>
<a name="id759868"></a>
<a class="link" href="asin.html#complex_number_tr1_algorithms.inverse_complex.asin.synopsis_">Synopsis:</a>
</h5>
<pre class="programlisting"><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>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">asin</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">z</span><span class="special">);</span>
@@ -50,7 +50,7 @@
</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 © 2005 John Maddock<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<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>
@@ -58,7 +58,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="implementation.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inverse_complex.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="acos.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>asinh</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
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<link rel="prev" href="atan.html" title="atan">
<link rel="next" href="acosh.html" title="acosh">
@@ -20,22 +20,22 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="atan.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../inverse_complex.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="acosh.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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<div class="section" lang="en">
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<a name="complex_number_tr1_algorithms.inverse_complex.asinh"></a><a href="asinh.html" title="asinh">
<a name="complex_number_tr1_algorithms.inverse_complex.asinh"></a><a class="link" href="asinh.html" title="asinh">
asinh</a>
</h3></div></div></div>
<a name="complex_number_tr1_algorithms.inverse_complex.asinh.header_"></a><h5>
<a name="id446106"></a>
<a href="asinh.html#complex_number_tr1_algorithms.inverse_complex.asinh.header_">Header:</a>
<a name="id760504"></a>
<a class="link" href="asinh.html#complex_number_tr1_algorithms.inverse_complex.asinh.header_">Header:</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">complex</span><span class="special">/</span><span class="identifier">asinh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<a name="complex_number_tr1_algorithms.inverse_complex.asinh.synopsis_"></a><h5>
<a name="id499790"></a>
<a href="asinh.html#complex_number_tr1_algorithms.inverse_complex.asinh.synopsis_">Synopsis:</a>
<a name="id760577"></a>
<a class="link" href="asinh.html#complex_number_tr1_algorithms.inverse_complex.asinh.synopsis_">Synopsis:</a>
</h5>
<pre class="programlisting"><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>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">asinh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">z</span><span class="special">);</span>
@@ -50,7 +50,7 @@
</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 © 2005 John Maddock<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<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>
@@ -58,7 +58,7 @@
</tr></table>
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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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<title>atan</title>
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@@ -20,22 +20,22 @@
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<a name="complex_number_tr1_algorithms.inverse_complex.atan"></a><a class="link" href="atan.html" title="atan">
atan</a>
</h3></div></div></div>
<a name="complex_number_tr1_algorithms.inverse_complex.atan.header_"></a><h5>
<a name="id445808"></a>
<a href="atan.html#complex_number_tr1_algorithms.inverse_complex.atan.header_">Header:</a>
<a name="id760268"></a>
<a class="link" href="atan.html#complex_number_tr1_algorithms.inverse_complex.atan.header_">Header:</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">complex</span><span class="special">/</span><span class="identifier">atan</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<a name="complex_number_tr1_algorithms.inverse_complex.atan.synopsis_"></a><h5>
<a name="id445901"></a>
<a href="atan.html#complex_number_tr1_algorithms.inverse_complex.atan.synopsis_">Synopsis:</a>
<a name="id760340"></a>
<a class="link" href="atan.html#complex_number_tr1_algorithms.inverse_complex.atan.synopsis_">Synopsis:</a>
</h5>
<pre class="programlisting"><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>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">atan</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">z</span><span class="special">);</span>
@@ -50,7 +50,7 @@
</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 © 2005 John Maddock<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<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>
@@ -58,7 +58,7 @@
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<hr>
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<link rel="next" href="history.html" title="History">
@@ -20,22 +20,22 @@
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<div class="titlepage"><div><div><h3 class="title">
<a name="complex_number_tr1_algorithms.inverse_complex.atanh"></a><a href="atanh.html" title="atanh">
<a name="complex_number_tr1_algorithms.inverse_complex.atanh"></a><a class="link" href="atanh.html" title="atanh">
atanh</a>
</h3></div></div></div>
<a name="complex_number_tr1_algorithms.inverse_complex.atanh.header_"></a><h5>
<a name="id500292"></a>
<a href="atanh.html#complex_number_tr1_algorithms.inverse_complex.atanh.header_">Header:</a>
<a name="id760977"></a>
<a class="link" href="atanh.html#complex_number_tr1_algorithms.inverse_complex.atanh.header_">Header:</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">complex</span><span class="special">/</span><span class="identifier">atanh</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<a name="complex_number_tr1_algorithms.inverse_complex.atanh.synopsis_"></a><h5>
<a name="id500385"></a>
<a href="atanh.html#complex_number_tr1_algorithms.inverse_complex.atanh.synopsis_">Synopsis:</a>
<a name="id761049"></a>
<a class="link" href="atanh.html#complex_number_tr1_algorithms.inverse_complex.atanh.synopsis_">Synopsis:</a>
</h5>
<pre class="programlisting"><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>
<span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">atanh</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="identifier">z</span><span class="special">);</span>
@@ -50,7 +50,7 @@
</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 © 2005 John Maddock<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<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>
@@ -58,7 +58,7 @@
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@@ -1,10 +1,10 @@
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@@ -19,24 +19,24 @@
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<a name="complex_number_tr1_algorithms.inverse_complex.history"></a><a href="history.html" title="History">History</a>
<a name="complex_number_tr1_algorithms.inverse_complex.history"></a><a class="link" href="history.html" title="History">History</a>
</h3></div></div></div>
<div class="itemizedlist"><ul type="disc">
<li>
2005/12/17: Added support for platforms with no meaningful numeric_limits&lt;&gt;::infinity().
</li>
<li>
2005/12/01: Initial version, added as part of the TR1 library.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
2005/12/17: Added support for platforms with no meaningful numeric_limits&lt;&gt;::infinity().
</li>
<li class="listitem">
2005/12/01: Initial version, added as part of the TR1 library.
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2005 John Maddock<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<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>
@@ -44,7 +44,7 @@
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<p>
@@ -47,7 +47,7 @@
</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 © 2005 John Maddock<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2005 John Maddock<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>
@@ -55,7 +55,7 @@
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@@ -17,7 +17,7 @@
</tr></table>
<hr>
<div class="spirit-nav"></div>
<div class="article" lang="en">
<div class="article">
<div class="titlepage">
<div>
<div><h2 class="title">
@@ -30,9 +30,9 @@
<span class="firstname">John</span> <span class="surname">Maddock</span>
</h3></div>
</div></div>
<div><p class="copyright">Copyright © 2008 Paul A. Bristow, John Maddock</p></div>
<div><p class="copyright">Copyright &#169; 2008 Paul A. Bristow, John Maddock</p></div>
<div><div class="legalnotice">
<a name="id770834"></a><p>
<a name="id759711"></a><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>
@@ -47,115 +47,115 @@
<p>
The distributions provided are:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
bernoulli
</li>
<li>
beta_distribution
</li>
<li>
binomial_distribution
</li>
<li>
cauchy
</li>
<li>
chi_squared
</li>
<li>
exponential
</li>
<li>
extreme_value
</li>
<li>
fisher_f
</li>
<li>
gamma_distribution
</li>
<li>
lognormal_distribution
</li>
<li>
negative_binomial_distribution
</li>
<li>
normal_distribution
</li>
<li>
pareto
</li>
<li>
poisson
</li>
<li>
rayleigh
</li>
<li>
students_t
</li>
<li>
triangular
</li>
<li>
uniform
</li>
<li>
weibull
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
bernoulli
</li>
<li class="listitem">
beta_distribution
</li>
<li class="listitem">
binomial_distribution
</li>
<li class="listitem">
cauchy
</li>
<li class="listitem">
chi_squared
</li>
<li class="listitem">
exponential
</li>
<li class="listitem">
extreme_value
</li>
<li class="listitem">
fisher_f
</li>
<li class="listitem">
gamma_distribution
</li>
<li class="listitem">
lognormal_distribution
</li>
<li class="listitem">
negative_binomial_distribution
</li>
<li class="listitem">
normal_distribution
</li>
<li class="listitem">
pareto
</li>
<li class="listitem">
poisson
</li>
<li class="listitem">
rayleigh
</li>
<li class="listitem">
students_t
</li>
<li class="listitem">
triangular
</li>
<li class="listitem">
uniform
</li>
<li class="listitem">
weibull
</li>
</ul></div>
<p>
Properties of distributions computed are:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
mean
</li>
<li>
mode
</li>
<li>
median
</li>
<li>
variance
</li>
<li>
standard deviation
</li>
<li>
coefficient of variation,
</li>
<li>
skewness
</li>
<li>
kurtosis
</li>
<li>
excess
</li>
<li>
range supported
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
mean
</li>
<li class="listitem">
mode
</li>
<li class="listitem">
median
</li>
<li class="listitem">
variance
</li>
<li class="listitem">
standard deviation
</li>
<li class="listitem">
coefficient of variation,
</li>
<li class="listitem">
skewness
</li>
<li class="listitem">
kurtosis
</li>
<li class="listitem">
excess
</li>
<li class="listitem">
range supported
</li>
</ul></div>
<p>
Calculated, from values provided, are:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
probability density (or mass) function (PDF)
</li>
<li>
cumulative distribution function (CDF), and complement
</li>
<li>
Quantiles (percentiles) are calculated for typical risk (alpha) probabilities
(0.001, 0.01, 0.5, 0.1, 0.333) and for additional probabilities provided by
the user.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
probability density (or mass) function (PDF)
</li>
<li class="listitem">
cumulative distribution function (CDF), and complement
</li>
<li class="listitem">
Quantiles (percentiles) are calculated for typical risk (alpha) probabilities
(0.001, 0.01, 0.5, 0.1, 0.333) and for additional probabilities provided
by the user.
</li>
</ul></div>
<p>
Results can be saved to text files using Save or SaveAs. All the values on the
@@ -207,7 +207,7 @@
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: February 26, 2009 at 17:08:18 GMT</small></p></td>
<td align="left"><p><small>Last revised: July 01, 2010 at 21:45:23 GMT</small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
</tr></table>
<hr>

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@@ -3,7 +3,7 @@
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LCM determination</a>
@@ -59,7 +59,7 @@
range of <code class="computeroutput"><span class="identifier">static_gcd_type</span></code>.
</p>
<a name="gcd_and_lcm.gcd_lcm.compile_time.example"></a><h4>
<a name="id923630"></a>
<a name="id761333"></a>
<a class="link" href="compile_time.html#gcd_and_lcm.gcd_lcm.compile_time.example">Example</a>
</h4>
<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">common_factor</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>

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@@ -3,7 +3,7 @@
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@@ -21,7 +21,7 @@
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<div class="itemizedlist"><ul type="disc">
<li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
17 Dec 2005: Converted documentation to Quickbook Format.
</li>
<li>
<li class="listitem">
2 Jul 2002: Compile-time and run-time items separated to new headers.
</li>
<li>
<li class="listitem">
7 Nov 2001: Initial version
</li>
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@@ -3,7 +3,7 @@
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<div><p class="copyright">Copyright &#169; 2001 -2002 Daryle Walker</p></div>
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<a name="id759702"></a><p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -42,7 +42,7 @@
<span class="firstname">Bruno</span> <span class="surname">Lalande</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Johan</span> <span class="surname">Råde</span>
<span class="firstname">Johan</span> <span class="surname">R&#229;de</span>
</h3></div>
<div class="author"><h3 class="author">
<span class="firstname">Gautam</span> <span class="surname">Sewani</span>
@@ -51,11 +51,11 @@
<span class="firstname">Thijs</span> <span class="surname">van den Berg</span>
</h3></div>
</div></div>
<div><p class="copyright">Copyright © 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Daryle Walker, Xiaogang Zhang, Bruno Lalande, Johan Råde,
<div><p class="copyright">Copyright &#169; 2006 , 2007, 2008, 2009 John Maddock, Paul A. Bristow,
Hubert Holin, Daryle Walker, Xiaogang Zhang, Bruno Lalande, Johan R&#229;de,
Gautam Sewani and Thijs van den Berg</p></div>
<div><div class="legalnotice">
<a name="id745444"></a><p>
<a name="id759784"></a><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>
@@ -73,249 +73,254 @@
</colgroup>
<thead><tr>
<th>
<p>
Library
</p>
<p>
Library
</p>
</th>
<th>
<p>
Description
</p>
<p>
Description
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
Complex Number Inverse Trigonometric Functions
</p>
<p>
<a href="../complex/html/index.html" target="_top">HTML Docs</a>
</p>
<p>
<a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/complex-tr1.pdf" target="_top">PDF
Docs</a>
</p>
<p>
Complex Number Inverse Trigonometric Functions
</p>
<p>
<a href="../complex/html/index.html" target="_top">HTML Docs</a>
</p>
<p>
<a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/complex-tr1.pdf" target="_top">PDF
Docs</a>
</p>
</td>
<td>
<p>
These complex number algorithms are the inverses of trigonometric functions
currently present in the C++ standard. Equivalents to these functions
are part of the C99 standard, and are part 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>.
</p>
<p>
These complex number algorithms are the inverses of trigonometric functions
currently present in the C++ standard. Equivalents to these functions
are part of the C99 standard, and are part 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>.
</p>
</td>
</tr>
<tr>
<td>
<p>
Greatest Common Divisor and Least Common Multiple
</p>
<p>
<a href="../gcd/html/index.html" target="_top">HTML Docs</a>
</p>
<p>
<a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/math-gcd.pdf" target="_top">PDF
Docs</a>
</p>
<p>
Greatest Common Divisor and Least Common Multiple
</p>
<p>
<a href="../gcd/html/index.html" target="_top">HTML Docs</a>
</p>
<p>
<a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/math-gcd.pdf" target="_top">PDF
Docs</a>
</p>
</td>
<td>
<p>
The class and function templates in &lt;boost/math/common_factor.hpp&gt;
provide run-time and compile-time evaluation of the greatest common divisor
(GCD) or least common multiple (LCM) of two integers. These facilities
are useful for many numeric-oriented generic programming problems.
</p>
<p>
The class and function templates in &lt;boost/math/common_factor.hpp&gt;
provide run-time and compile-time evaluation of the greatest common
divisor (GCD) or least common multiple (LCM) of two integers. These
facilities are useful for many numeric-oriented generic programming
problems.
</p>
</td>
</tr>
<tr>
<td>
<p>
Octonions
</p>
<p>
<a href="../octonion/html/index.html" target="_top">HTML Docs</a>
</p>
<p>
<a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/octonion.pdf" target="_top">PDF
Docs</a>
</p>
<p>
Octonions
</p>
<p>
<a href="../octonion/html/index.html" target="_top">HTML Docs</a>
</p>
<p>
<a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/octonion.pdf" target="_top">PDF
Docs</a>
</p>
</td>
<td>
<p>
Octonions, like <a href="../quaternion/html/index.html" target="_top">quaternions</a>,
are a relative of complex numbers.
</p>
<p>
Octonions see some use in theoretical physics.
</p>
<p>
In practical terms, an octonion is simply an octuple of real numbers
(&#945;,&#946;,&#947;,&#948;,&#949;,&#950;,&#951;,&#952;), which we can write in the form <span class="emphasis"><em><code class="literal">o = &#945; + &#946;i + &#947;j + &#948;k + &#949;e' + &#950;i' + &#951;j' + &#952;k'</code></em></span>,
where <span class="emphasis"><em><code class="literal">i</code></em></span>, <span class="emphasis"><em><code class="literal">j</code></em></span>
and <span class="emphasis"><em><code class="literal">k</code></em></span> are the same objects as
for quaternions, and <span class="emphasis"><em><code class="literal">e'</code></em></span>, <span class="emphasis"><em><code class="literal">i'</code></em></span>,
<span class="emphasis"><em><code class="literal">j'</code></em></span> and <span class="emphasis"><em><code class="literal">k'</code></em></span>
are distinct objects which play essentially the same kind of role as
<span class="emphasis"><em><code class="literal">i</code></em></span> (or <span class="emphasis"><em><code class="literal">j</code></em></span>
or <span class="emphasis"><em><code class="literal">k</code></em></span>).
</p>
<p>
Addition and a multiplication is defined on the set of octonions, which
generalize their quaternionic counterparts. The main novelty this time
is that <span class="bold"><strong>the multiplication is not only not commutative,
is now not even associative</strong></span> (i.e. there are quaternions <span class="emphasis"><em><code class="literal">x</code></em></span>,
<span class="emphasis"><em><code class="literal">y</code></em></span> and <span class="emphasis"><em><code class="literal">z</code></em></span>
such that <span class="emphasis"><em><code class="literal">x(yz) &#8800; (xy)z</code></em></span>). A way
of remembering things is by using the following multiplication table:
</p>
<p>
<span class="inlinemediaobject"><img src="../../octonion/graphics/octonion_blurb17.jpeg" alt="octonion_blurb17"></span>
</p>
<p>
Octonions (and their kin) are described in far more details in this other
<a href="../../quaternion/TQE.pdf" target="_top">document</a> (with <a href="../../quaternion/TQE_EA.pdf" target="_top">errata
and addenda</a>).
</p>
<p>
Some traditional constructs, such as the exponential, carry over without
too much change into the realms of octonions, but other, such as taking
a square root, do not (the fact that the exponential has a closed form
is a result of the author, but the fact that the exponential exists at
all for octonions is known since quite a long time ago).
</p>
<p>
Octonions, like <a href="../quaternion/html/index.html" target="_top">quaternions</a>,
are a relative of complex numbers.
</p>
<p>
Octonions see some use in theoretical physics.
</p>
<p>
In practical terms, an octonion is simply an octuple of real numbers
(&#945;,&#946;,&#947;,&#948;,&#949;,&#950;,&#951;,&#952;), which we can write in the form <span class="emphasis"><em><code class="literal">o = &#945; + &#946;i + &#947;j + &#948;k + &#949;e' + &#950;i' + &#951;j' + &#952;k'</code></em></span>,
where <span class="emphasis"><em><code class="literal">i</code></em></span>, <span class="emphasis"><em><code class="literal">j</code></em></span>
and <span class="emphasis"><em><code class="literal">k</code></em></span> are the same objects
as for quaternions, and <span class="emphasis"><em><code class="literal">e'</code></em></span>,
<span class="emphasis"><em><code class="literal">i'</code></em></span>, <span class="emphasis"><em><code class="literal">j'</code></em></span>
and <span class="emphasis"><em><code class="literal">k'</code></em></span> are distinct objects
which play essentially the same kind of role as <span class="emphasis"><em><code class="literal">i</code></em></span>
(or <span class="emphasis"><em><code class="literal">j</code></em></span> or <span class="emphasis"><em><code class="literal">k</code></em></span>).
</p>
<p>
Addition and a multiplication is defined on the set of octonions, which
generalize their quaternionic counterparts. The main novelty this time
is that <span class="bold"><strong>the multiplication is not only not commutative,
is now not even associative</strong></span> (i.e. there are quaternions
<span class="emphasis"><em><code class="literal">x</code></em></span>, <span class="emphasis"><em><code class="literal">y</code></em></span>
and <span class="emphasis"><em><code class="literal">z</code></em></span> such that <span class="emphasis"><em><code class="literal">x(yz)
&#8800; (xy)z</code></em></span>). A way of remembering things is by using
the following multiplication table:
</p>
<p>
<span class="inlinemediaobject"><img src="../../octonion/graphics/octonion_blurb17.jpeg" alt="octonion_blurb17"></span>
</p>
<p>
Octonions (and their kin) are described in far more details in this
other <a href="../../quaternion/TQE.pdf" target="_top">document</a> (with
<a href="../../quaternion/TQE_EA.pdf" target="_top">errata and addenda</a>).
</p>
<p>
Some traditional constructs, such as the exponential, carry over without
too much change into the realms of octonions, but other, such as taking
a square root, do not (the fact that the exponential has a closed form
is a result of the author, but the fact that the exponential exists
at all for octonions is known since quite a long time ago).
</p>
</td>
</tr>
<tr>
<td>
<p>
Special Functions
</p>
<p>
<a href="../sf_and_dist/html/index.html" target="_top">HTML Docs</a>
</p>
<p>
<a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/math.pdf" target="_top">PDF
Docs</a>
</p>
<p>
Special Functions
</p>
<p>
<a href="../sf_and_dist/html/index.html" target="_top">HTML Docs</a>
</p>
<p>
<a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/math.pdf" target="_top">PDF
Docs</a>
</p>
</td>
<td>
<p>
Provides a number of high quality special functions, initially these
were concentrated on functions used in statistical applications along
with those in the Technical Report on C++ Library Extensions.
</p>
<p>
The function families currently implemented are the gamma, beta &amp;
erf functions along with the incomplete gamma and beta functions (four
variants of each) and all the possible inverses of these, plus digamma,
various factorial functions, Bessel functions, elliptic integrals, sinus
cardinals (along with their hyperbolic variants), inverse hyperbolic
functions, Legrendre/Laguerre/Hermite polynomials and various special
power and logarithmic functions.
</p>
<p>
All the implementations are fully generic and support the use of arbitrary
"real-number" types, although they are optimised for use with
types with known-about significand (or mantissa) sizes: typically float,
double or long double.
</p>
<p>
Provides a number of high quality special functions, initially these
were concentrated on functions used in statistical applications along
with those in the Technical Report on C++ Library Extensions.
</p>
<p>
The function families currently implemented are the gamma, beta &amp;
erf functions along with the incomplete gamma and beta functions (four
variants of each) and all the possible inverses of these, plus digamma,
various factorial functions, Bessel functions, elliptic integrals,
sinus cardinals (along with their hyperbolic variants), inverse hyperbolic
functions, Legrendre/Laguerre/Hermite polynomials and various special
power and logarithmic functions.
</p>
<p>
All the implementations are fully generic and support the use of arbitrary
"real-number" types, although they are optimised for use
with types with known-about significand (or mantissa) sizes: typically
float, double or long double.
</p>
</td>
</tr>
<tr>
<td>
<p>
Statistical Distributions
</p>
<p>
<a href="../sf_and_dist/html/index.html" target="_top">HTML Docs</a>
</p>
<p>
<a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/math.pdf" target="_top">PDF
Docs</a>
</p>
<p>
Statistical Distributions
</p>
<p>
<a href="../sf_and_dist/html/index.html" target="_top">HTML Docs</a>
</p>
<p>
<a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/math.pdf" target="_top">PDF
Docs</a>
</p>
</td>
<td>
<p>
Provides a reasonably comprehensive set of statistical distributions,
upon which higher level statistical tests can be built.
</p>
<p>
The initial focus is on the central univariate distributions. Both continuous
(like normal &amp; Fisher) and discrete (like binomial &amp; Poisson)
distributions are provided.
</p>
<p>
A comprehensive tutorial is provided, along with a series of worked examples
illustrating how the library is used to conduct statistical tests.
</p>
<p>
Provides a reasonably comprehensive set of statistical distributions,
upon which higher level statistical tests can be built.
</p>
<p>
The initial focus is on the central univariate distributions. Both
continuous (like normal &amp; Fisher) and discrete (like binomial &amp;
Poisson) distributions are provided.
</p>
<p>
A comprehensive tutorial is provided, along with a series of worked
examples illustrating how the library is used to conduct statistical
tests.
</p>
</td>
</tr>
<tr>
<td>
<p>
Quaternions
</p>
<p>
<a href="../quaternion/html/index.html" target="_top">HTML Docs</a>
</p>
<p>
<a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/quaternion.pdf" target="_top">PDF
Docs</a>
</p>
<p>
Quaternions
</p>
<p>
<a href="../quaternion/html/index.html" target="_top">HTML Docs</a>
</p>
<p>
<a href="http://svn.boost.org/svn/boost/sandbox/pdf/math/release/quaternion.pdf" target="_top">PDF
Docs</a>
</p>
</td>
<td>
<p>
Quaternions are a relative of complex numbers.
</p>
<p>
Quaternions are in fact part of a small hierarchy of structures built
upon the real numbers, which comprise only the set of real numbers (traditionally
named <span class="emphasis"><em><span class="bold"><strong>R</strong></span></em></span>), the set
of complex numbers (traditionally named <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span>),
the set of quaternions (traditionally named <span class="emphasis"><em><span class="bold"><strong>H</strong></span></em></span>)
and the set of octonions (traditionally named <span class="emphasis"><em><span class="bold"><strong>O</strong></span></em></span>),
which possess interesting mathematical properties (chief among which
is the fact that they are <span class="emphasis"><em>division algebras</em></span>, <span class="emphasis"><em>i.e.</em></span>
where the following property is true: if <span class="emphasis"><em><code class="literal">y</code></em></span>
is an element of that algebra and is <span class="bold"><strong>not equal
to zero</strong></span>, then <span class="emphasis"><em><code class="literal">yx = yx'</code></em></span>,
where <span class="emphasis"><em><code class="literal">x</code></em></span> and <span class="emphasis"><em><code class="literal">x'</code></em></span>
denote elements of that algebra, implies that <span class="emphasis"><em><code class="literal">x =
x'</code></em></span>). Each member of the hierarchy is a super-set
of the former.
</p>
<p>
One of the most important aspects of quaternions is that they provide
an efficient way to parameterize rotations in <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span>
(the usual three-dimensional space) and <span class="emphasis"><em><span class="bold"><strong>R<sup>4</sup></strong></span></em></span>.
</p>
<p>
In practical terms, a quaternion is simply a quadruple of real numbers
(&#945;,&#946;,&#947;,&#948;), which we can write in the form <span class="emphasis"><em><code class="literal">q = &#945; + &#946;i + &#947;j + &#948;k</code></em></span>,
where <span class="emphasis"><em><code class="literal">i</code></em></span> is the same object as
for complex numbers, and <span class="emphasis"><em><code class="literal">j</code></em></span> and
<span class="emphasis"><em><code class="literal">k</code></em></span> are distinct objects which
play essentially the same kind of role as <span class="emphasis"><em><code class="literal">i</code></em></span>.
</p>
<p>
An addition and a multiplication is defined on the set of quaternions,
which generalize their real and complex counterparts. The main novelty
here is that <span class="bold"><strong>the multiplication is not commutative</strong></span>
(i.e. there are quaternions <span class="emphasis"><em><code class="literal">x</code></em></span>
and <span class="emphasis"><em><code class="literal">y</code></em></span> such that <span class="emphasis"><em><code class="literal">xy
&#8800; yx</code></em></span>). A good mnemotechnical way of remembering things
is by using the formula <span class="emphasis"><em><code class="literal">i*i = j*j = k*k = -1</code></em></span>.
</p>
<p>
Quaternions (and their kin) are described in far more details in this
other <a href="../../quaternion/TQE.pdf" target="_top">document</a> (with <a href="../../quaternion/TQE_EA.pdf" target="_top">errata and addenda</a>).
</p>
<p>
Some traditional constructs, such as the exponential, carry over without
too much change into the realms of quaternions, but other, such as taking
a square root, do not.
</p>
<p>
Quaternions are a relative of complex numbers.
</p>
<p>
Quaternions are in fact part of a small hierarchy of structures built
upon the real numbers, which comprise only the set of real numbers
(traditionally named <span class="emphasis"><em><span class="bold"><strong>R</strong></span></em></span>),
the set of complex numbers (traditionally named <span class="emphasis"><em><span class="bold"><strong>C</strong></span></em></span>), the set of quaternions (traditionally
named <span class="emphasis"><em><span class="bold"><strong>H</strong></span></em></span>) and
the set of octonions (traditionally named <span class="emphasis"><em><span class="bold"><strong>O</strong></span></em></span>),
which possess interesting mathematical properties (chief among which
is the fact that they are <span class="emphasis"><em>division algebras</em></span>,
<span class="emphasis"><em>i.e.</em></span> where the following property is true: if
<span class="emphasis"><em><code class="literal">y</code></em></span> is an element of that algebra
and is <span class="bold"><strong>not equal to zero</strong></span>, then <span class="emphasis"><em><code class="literal">yx
= yx'</code></em></span>, where <span class="emphasis"><em><code class="literal">x</code></em></span>
and <span class="emphasis"><em><code class="literal">x'</code></em></span> denote elements of that
algebra, implies that <span class="emphasis"><em><code class="literal">x = x'</code></em></span>).
Each member of the hierarchy is a super-set of the former.
</p>
<p>
One of the most important aspects of quaternions is that they provide
an efficient way to parameterize rotations in <span class="emphasis"><em><span class="bold"><strong>R<sup>3</sup></strong></span></em></span>
(the usual three-dimensional space) and <span class="emphasis"><em><span class="bold"><strong>R<sup>4</sup></strong></span></em></span>.
</p>
<p>
In practical terms, a quaternion is simply a quadruple of real numbers
(&#945;,&#946;,&#947;,&#948;), which we can write in the form <span class="emphasis"><em><code class="literal">q = &#945; + &#946;i + &#947;j + &#948;k</code></em></span>,
where <span class="emphasis"><em><code class="literal">i</code></em></span> is the same object
as for complex numbers, and <span class="emphasis"><em><code class="literal">j</code></em></span>
and <span class="emphasis"><em><code class="literal">k</code></em></span> are distinct objects
which play essentially the same kind of role as <span class="emphasis"><em><code class="literal">i</code></em></span>.
</p>
<p>
An addition and a multiplication is defined on the set of quaternions,
which generalize their real and complex counterparts. The main novelty
here is that <span class="bold"><strong>the multiplication is not commutative</strong></span>
(i.e. there are quaternions <span class="emphasis"><em><code class="literal">x</code></em></span>
and <span class="emphasis"><em><code class="literal">y</code></em></span> such that <span class="emphasis"><em><code class="literal">xy
&#8800; yx</code></em></span>). A good mnemotechnical way of remembering
things is by using the formula <span class="emphasis"><em><code class="literal">i*i = j*j = k*k =
-1</code></em></span>.
</p>
<p>
Quaternions (and their kin) are described in far more details in this
other <a href="../../quaternion/TQE.pdf" target="_top">document</a> (with
<a href="../../quaternion/TQE_EA.pdf" target="_top">errata and addenda</a>).
</p>
<p>
Some traditional constructs, such as the exponential, carry over without
too much change into the realms of quaternions, but other, such as
taking a square root, do not.
</p>
</td>
</tr>
</tbody>
@@ -330,133 +335,133 @@
</colgroup>
<thead><tr>
<th>
<p>
Library
</p>
<p>
Library
</p>
</th>
<th>
<p>
Description
</p>
<p>
Description
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<a href="../../../integer/index.html" target="_top">Integer</a>
</p>
<p>
<a href="../../../integer/index.html" target="_top">Integer</a>
</p>
</td>
<td>
<p>
Headers to ease dealing with integral types.
</p>
<p>
Headers to ease dealing with integral types.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a href="../../../numeric/interval/doc/interval.htm" target="_top">Interval</a>
</p>
<p>
<a href="../../../numeric/interval/doc/interval.htm" target="_top">Interval</a>
</p>
</td>
<td>
<p>
As implied by its name, this library is intended to help manipulating
mathematical intervals. It consists of a single header &lt;boost/numeric/interval.hpp&gt;
and principally a type which can be used as interval&lt;T&gt;.
</p>
<p>
As implied by its name, this library is intended to help manipulating
mathematical intervals. It consists of a single header &lt;boost/numeric/interval.hpp&gt;
and principally a type which can be used as interval&lt;T&gt;.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a href="../../../multi_array/doc/index.html" target="_top">Multi Array</a>
</p>
<p>
<a href="../../../multi_array/doc/index.html" target="_top">Multi Array</a>
</p>
</td>
<td>
<p>
Boost.MultiArray provides a generic N-dimensional array concept definition
and common implementations of that interface.
</p>
<p>
Boost.MultiArray provides a generic N-dimensional array concept definition
and common implementations of that interface.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a href="../../../numeric/conversion/index.html" target="_top">Numeric.Conversion</a>
</p>
<p>
<a href="../../../numeric/conversion/index.html" target="_top">Numeric.Conversion</a>
</p>
</td>
<td>
<p>
The Boost Numeric Conversion library is a collection of tools to describe
and perform conversions between values of different numeric types.
</p>
<p>
The Boost Numeric Conversion library is a collection of tools to describe
and perform conversions between values of different numeric types.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a href="../../../utility/operators.htm" target="_top">Operators</a>
</p>
<p>
<a href="../../../utility/operators.htm" target="_top">Operators</a>
</p>
</td>
<td>
<p>
The header &lt;boost/operators.hpp&gt; supplies several sets of class
templates (in namespace boost). These templates define operators at namespace
scope in terms of a minimal number of fundamental operators provided
by the class.
</p>
<p>
The header &lt;boost/operators.hpp&gt; supplies several sets of class
templates (in namespace boost). These templates define operators at
namespace scope in terms of a minimal number of fundamental operators
provided by the class.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a href="../../../random/index.html" target="_top">Random</a>
</p>
<p>
<a href="../../../random/index.html" target="_top">Random</a>
</p>
</td>
<td>
<p>
Random numbers are useful in a variety of applications. The Boost Random
Number Library (Boost.Random for short) provides a vast variety of generators
and distributions to produce random numbers having useful properties,
such as uniform distribution.
</p>
<p>
Random numbers are useful in a variety of applications. The Boost Random
Number Library (Boost.Random for short) provides a vast variety of
generators and distributions to produce random numbers having useful
properties, such as uniform distribution.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a href="../../../rational/index.html" target="_top">Rational</a>
</p>
<p>
<a href="../../../rational/index.html" target="_top">Rational</a>
</p>
</td>
<td>
<p>
The header rational.hpp provides an implementation of rational numbers.
The implementation is template-based, in a similar manner to the standard
complex number class.
</p>
<p>
The header rational.hpp provides an implementation of rational numbers.
The implementation is template-based, in a similar manner to the standard
complex number class.
</p>
</td>
</tr>
<tr>
<td>
<p>
<a href="../../../numeric/ublas/doc/index.htm" target="_top">uBLAS</a>
</p>
<p>
<a href="../../../numeric/ublas/doc/index.htm" target="_top">uBLAS</a>
</p>
</td>
<td>
<p>
uBLAS is a C++ template class library that provides BLAS level 1, 2,
3 functionality for dense, packed and sparse matrices. The design and
implementation unify mathematical notation via operator overloading and
efficient code generation via expression templates.
</p>
<p>
uBLAS is a C++ template class library that provides BLAS level 1, 2,
3 functionality for dense, packed and sparse matrices. The design and
implementation unify mathematical notation via operator overloading
and efficient code generation via expression templates.
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: May 28, 2008 at 10:39:25 +0100</small></p></td>
<td align="left"><p><small>Last revised: , at </small></p></td>
<td align="right"><div class="copyright-footer"></div></td>
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<div class="toc"><dl>
<dt><span class="section"><a href="octonions/overview.html">Overview</a></span></dt>
@@ -54,7 +54,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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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@@ -62,7 +62,7 @@
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<a name="boost_octonions.octonions.acknowledgements"></a><a href="acknowledgements.html" title="Acknowledgements">Acknowledgements</a>
<a name="boost_octonions.octonions.acknowledgements"></a><a class="link" href="acknowledgements.html" title="Acknowledgements">Acknowledgements</a>
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<p>
The mathematical text has been typeset with <a href="http://www.nisus-soft.com/" target="_top">Nisus
@@ -36,7 +36,7 @@
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<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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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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@@ -44,7 +44,7 @@
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@@ -20,11 +20,11 @@
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<a name="boost_octonions.octonions.header_file"></a><a class="link" href="header_file.html" title="Header File">Header File</a>
</h3></div></div></div>
<p>
The interface and implementation are both supplied by the header file <a href="../../../../../../../boost/math/octonion.hpp" target="_top">octonion.hpp</a>.
@@ -32,7 +32,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -40,7 +40,7 @@
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@@ -20,78 +20,82 @@
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<a name="boost_octonions.octonions.history"></a><a href="history.html" title="History">History</a>
<a name="boost_octonions.octonions.history"></a><a class="link" href="history.html" title="History">History</a>
</h3></div></div></div>
<div class="itemizedlist"><ul type="disc">
<li>
1.5.8 - 17/12/2005: Converted documentation to Quickbook Format.
</li>
<li>
1.5.7 - 25/02/2003: transitionned to the unit test framework; &lt;boost/config.hpp&gt;
now included by the library header (rather than the test files), via &lt;boost/math/quaternion.hpp&gt;.
</li>
<li>
1.5.6 - 15/10/2002: Gcc2.95.x and stlport on linux compatibility by Alkis
Evlogimenos (alkis@routescience.com).
</li>
<li>
1.5.5 - 27/09/2002: Microsoft VCPP 7 compatibility, by Michael Stevens
(michael@acfr.usyd.edu.au); requires the /Za compiler option.
</li>
<li>
1.5.4 - 19/09/2002: fixed problem with multiple inclusion (in different
translation units); attempt at an improved compatibility with Microsoft
compilers, by Michael Stevens (michael@acfr.usyd.edu.au) and Fredrik Blomqvist;
other compatibility fixes.
</li>
<li>
1.5.3 - 01/02/2002: bugfix and Gcc 2.95.3 compatibility by Douglas Gregor
(gregod@cs.rpi.edu).
</li>
<li>
1.5.2 - 07/07/2001: introduced namespace math.
</li>
<li>
1.5.1 - 07/06/2001: (end of Boost review) now includes &lt;boost/math/special_functions/sinc.hpp&gt;
and &lt;boost/math/special_functions/sinhc.hpp&gt; instead of &lt;boost/special_functions.hpp&gt;;
corrected bug in sin (Daryle Walker); removed check for self-assignment
(Gary Powel); made converting functions explicit (Gary Powel); added overflow
guards for division operators and abs (Peter Schmitteckert); added sup
and l1; used Vesa Karvonen's CPP metaprograming technique to simplify code.
</li>
<li>
1.5.0 - 23/03/2001: boostification, inlining of all operators except input,
output and pow, fixed exception safety of some members (template version).
</li>
<li>
1.4.0 - 09/01/2001: added tan and tanh.
</li>
<li>
1.3.1 - 08/01/2001: cosmetic fixes.
</li>
<li>
1.3.0 - 12/07/2000: pow now uses Maarten Hilferink's (mhilferink@tip.nl)
algorithm.
</li>
<li>
1.2.0 - 25/05/2000: fixed the division operators and output; changed many
signatures.
</li>
<li>
1.1.0 - 23/05/2000: changed sinc into sinc_pi; added sin, cos, sinh, cosh.
</li>
<li>
1.0.0 - 10/08/1999: first public version.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
1.5.8 - 17/12/2005: Converted documentation to Quickbook Format.
</li>
<li class="listitem">
1.5.7 - 25/02/2003: transitionned to the unit test framework; &lt;boost/config.hpp&gt;
now included by the library header (rather than the test files), via
&lt;boost/math/quaternion.hpp&gt;.
</li>
<li class="listitem">
1.5.6 - 15/10/2002: Gcc2.95.x and stlport on linux compatibility by Alkis
Evlogimenos (alkis@routescience.com).
</li>
<li class="listitem">
1.5.5 - 27/09/2002: Microsoft VCPP 7 compatibility, by Michael Stevens
(michael@acfr.usyd.edu.au); requires the /Za compiler option.
</li>
<li class="listitem">
1.5.4 - 19/09/2002: fixed problem with multiple inclusion (in different
translation units); attempt at an improved compatibility with Microsoft
compilers, by Michael Stevens (michael@acfr.usyd.edu.au) and Fredrik
Blomqvist; other compatibility fixes.
</li>
<li class="listitem">
1.5.3 - 01/02/2002: bugfix and Gcc 2.95.3 compatibility by Douglas Gregor
(gregod@cs.rpi.edu).
</li>
<li class="listitem">
1.5.2 - 07/07/2001: introduced namespace math.
</li>
<li class="listitem">
1.5.1 - 07/06/2001: (end of Boost review) now includes &lt;boost/math/special_functions/sinc.hpp&gt;
and &lt;boost/math/special_functions/sinhc.hpp&gt; instead of &lt;boost/special_functions.hpp&gt;;
corrected bug in sin (Daryle Walker); removed check for self-assignment
(Gary Powel); made converting functions explicit (Gary Powel); added
overflow guards for division operators and abs (Peter Schmitteckert);
added sup and l1; used Vesa Karvonen's CPP metaprograming technique to
simplify code.
</li>
<li class="listitem">
1.5.0 - 23/03/2001: boostification, inlining of all operators except
input, output and pow, fixed exception safety of some members (template
version).
</li>
<li class="listitem">
1.4.0 - 09/01/2001: added tan and tanh.
</li>
<li class="listitem">
1.3.1 - 08/01/2001: cosmetic fixes.
</li>
<li class="listitem">
1.3.0 - 12/07/2000: pow now uses Maarten Hilferink's (mhilferink@tip.nl)
algorithm.
</li>
<li class="listitem">
1.2.0 - 25/05/2000: fixed the division operators and output; changed
many signatures.
</li>
<li class="listitem">
1.1.0 - 23/05/2000: changed sinc into sinc_pi; added sin, cos, sinh,
cosh.
</li>
<li class="listitem">
1.0.0 - 10/08/1999: first public version.
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -99,7 +103,7 @@
</tr></table>
<hr>
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Octonion Non-Member Operators</title>
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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_octonions.octonions.non_mem"></a><a href="non_mem.html" title="Octonion Non-Member Operators"> Octonion Non-Member
<a name="boost_octonions.octonions.non_mem"></a><a class="link" href="non_mem.html" title="Octonion Non-Member Operators"> Octonion Non-Member
Operators</a>
</h3></div></div></div>
<a name="boost_octonions.octonions.non_mem.unary_plus_and_minus_operators"></a><h5>
<a name="id533169"></a>
<a href="non_mem.html#boost_octonions.octonions.non_mem.unary_plus_and_minus_operators">Unary
<a name="id789630"></a>
<a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.unary_plus_and_minus_operators">Unary
Plus and Minus Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
@@ -43,8 +43,8 @@
This unary operator returns the opposite of o.
</p>
<a name="boost_octonions.octonions.non_mem.binary_addition_operators"></a><h5>
<a name="id533438"></a>
<a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">Binary
<a name="id789867"></a>
<a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">Binary
Addition Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
@@ -60,8 +60,8 @@
<span class="identifier">rhs</span></code>.
</p>
<a name="boost_octonions.octonions.non_mem.binary_subtraction_operators"></a><h5>
<a name="id534657"></a>
<a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">Binary
<a name="id790941"></a>
<a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">Binary
Subtraction Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
@@ -77,8 +77,8 @@
<span class="identifier">rhs</span></code>.
</p>
<a name="boost_octonions.octonions.non_mem.binary_multiplication_operators"></a><h5>
<a name="id535876"></a>
<a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">Binary
<a name="id792016"></a>
<a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">Binary
Multiplication Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
@@ -94,8 +94,8 @@
<span class="identifier">rhs</span></code>.
</p>
<a name="boost_octonions.octonions.non_mem.binary_division_operators"></a><h5>
<a name="id537095"></a>
<a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">Binary
<a name="id793089"></a>
<a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">Binary
Division Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
@@ -112,8 +112,8 @@
to divide by zero...
</p>
<a name="boost_octonions.octonions.non_mem.binary_equality_operators"></a><h5>
<a name="id538314"></a>
<a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">Binary
<a name="id794164"></a>
<a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">Binary
Equality Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
@@ -130,8 +130,8 @@
with any floating-type entity, this is essentially meaningless.
</p>
<a name="boost_octonions.octonions.non_mem.binary_inequality_operators"></a><h5>
<a name="id539450"></a>
<a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">Binary
<a name="id795169"></a>
<a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">Binary
Inequality Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
@@ -148,8 +148,8 @@
false. As with any floating-type entity, this is essentially meaningless.
</p>
<a name="boost_octonions.octonions.non_mem.stream_extractor"></a><h5>
<a name="id540589"></a>
<a href="non_mem.html#boost_octonions.octonions.non_mem.stream_extractor">Stream
<a name="id796174"></a>
<a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.stream_extractor">Stream
Extractor</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
@@ -170,8 +170,8 @@
Returns <code class="computeroutput"><span class="identifier">is</span></code>.
</p>
<a name="boost_octonions.octonions.non_mem.stream_inserter"></a><h5>
<a name="id540954"></a>
<a href="non_mem.html#boost_octonions.octonions.non_mem.stream_inserter">Stream
<a name="id796500"></a>
<a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.stream_inserter">Stream
Inserter</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
@@ -207,7 +207,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -215,7 +215,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="octonion_member_functions.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonion_value_operations.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Octonion Creation Functions</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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@@ -20,11 +20,11 @@
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<div class="section" lang="en">
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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_octonions.octonions.oct_create"></a><a href="oct_create.html" title="Octonion Creation Functions"> Octonion Creation
<a name="boost_octonions.octonions.oct_create"></a><a class="link" href="oct_create.html" title="Octonion Creation Functions"> Octonion Creation
Functions</a>
</h3></div></div></div>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">spherical</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi6</span><span class="special">);</span>
@@ -68,7 +68,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -76,7 +76,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="octonion_value_operations.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonions_transcendentals.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="octonion_value_operations.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.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="octonions_transcendentals.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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View File

@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Octonion Member Functions</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" href="../../index.html" title="Boost.Octonions">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Boost.Octonions">
<link rel="up" href="../octonions.html" title="Octonions">
<link rel="prev" href="octonion_member_typedefs.html" title="Octonion Member Typedefs">
<link rel="next" href="non_mem.html" title="Octonion Non-Member Operators">
@@ -20,16 +20,16 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="octonion_member_typedefs.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="non_mem.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_octonions.octonions.octonion_member_functions"></a><a href="octonion_member_functions.html" title="Octonion Member Functions">Octonion
<a name="boost_octonions.octonions.octonion_member_functions"></a><a class="link" href="octonion_member_functions.html" title="Octonion Member Functions">Octonion
Member Functions</a>
</h3></div></div></div>
<a name="boost_octonions.octonions.octonion_member_functions.constructors"></a><h4>
<a name="id525451"></a>
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">Constructors</a>
<a name="id782528"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">Constructors</a>
</h4>
<p>
Template version:
@@ -85,13 +85,13 @@
function in a "detail" subnamespace.
</p>
<a name="boost_octonions.octonions.octonion_member_functions.other_member_functions"></a><h4>
<a name="id529803"></a>
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_functions">Other
<a name="id786632"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_functions">Other
member functions</a>
</h4>
<a name="boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts"></a><h5>
<a name="id529829"></a>
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">Real
<a name="id786654"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">Real
and Unreal Parts</a>
</h5>
<pre class="programlisting"><span class="identifier">T</span> <span class="identifier">real</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
@@ -105,8 +105,8 @@
These are returned by the first two functions.
</p>
<a name="boost_octonions.octonions.octonion_member_functions.individual_real_components"></a><h5>
<a name="id529936"></a>
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">Individual
<a name="id786755"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">Individual
Real Components</a>
</h5>
<pre class="programlisting"><span class="identifier">T</span> <span class="identifier">R_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
@@ -123,8 +123,8 @@
functions. Hence real and R_component_1 return the same value.
</p>
<a name="boost_octonions.octonions.octonion_member_functions.individual_complex_components"></a><h5>
<a name="id530199"></a>
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">Individual
<a name="id786990"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">Individual
Complex Components</a>
</h5>
<pre class="programlisting"><span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">C_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
@@ -143,8 +143,8 @@
the basis <span class="emphasis"><em><code class="literal">(1, j, e', j')</code></em></span>.
</p>
<a name="boost_octonions.octonions.octonion_member_functions.individual_quaternion_components"></a><h5>
<a name="id530512"></a>
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">Individual
<a name="id787271"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">Individual
Quaternion Components</a>
</h5>
<pre class="programlisting"><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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">H_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
@@ -158,13 +158,13 @@
to build the octonion using the constructor.
</p>
<a name="boost_octonions.octonions.octonion_member_functions.octonion_member_operators"></a><h4>
<a name="id530704"></a>
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.octonion_member_operators">Octonion
<a name="id787445"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.octonion_member_operators">Octonion
Member Operators</a>
</h4>
<a name="boost_octonions.octonions.octonion_member_functions.assignment_operators"></a><h5>
<a name="id530730"></a>
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">Assignment
<a name="id787468"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">Assignment
Operators</a>
</h5>
<pre class="programlisting"><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
@@ -181,8 +181,8 @@
base type's assignment operators must not throw.
</p>
<a name="boost_octonions.octonions.octonion_member_functions.other_member_operators"></a><h5>
<a name="id531259"></a>
<a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">Other
<a name="id787939"></a>
<a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">Other
Member Operators</a>
</h5>
<pre class="programlisting"><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span>
@@ -246,7 +246,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -254,7 +254,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="octonion_member_typedefs.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="non_mem.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="octonion_member_typedefs.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.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="non_mem.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Octonion Member Typedefs</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" href="../../index.html" title="Boost.Octonions">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
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<link rel="up" href="../octonions.html" title="Octonions">
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<link rel="next" href="octonion_member_functions.html" title="Octonion Member Functions">
@@ -20,11 +20,11 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="octonion_specializations.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonion_member_functions.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_octonions.octonions.octonion_member_typedefs"></a><a href="octonion_member_typedefs.html" title="Octonion Member Typedefs">Octonion
<a name="boost_octonions.octonions.octonion_member_typedefs"></a><a class="link" href="octonion_member_typedefs.html" title="Octonion Member Typedefs">Octonion
Member Typedefs</a>
</h3></div></div></div>
<p>
@@ -56,7 +56,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -64,7 +64,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="octonion_specializations.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonion_member_functions.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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@@ -1,10 +1,10 @@
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<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
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<link rel="next" href="octonion_member_typedefs.html" title="Octonion Member Typedefs">
@@ -20,11 +20,11 @@
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<hr>
<div class="spirit-nav">
<a accesskey="p" href="template_class_octonion.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonion_member_typedefs.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_octonions.octonions.octonion_specializations"></a><a href="octonion_specializations.html" title="Octonion Specializations">Octonion
<a name="boost_octonions.octonions.octonion_specializations"></a><a class="link" href="octonion_specializations.html" title="Octonion Specializations">Octonion
Specializations</a>
</h3></div></div></div>
<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>
@@ -35,62 +35,62 @@
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="keyword">float</span> <span class="identifier">value_type</span><span class="special">;</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">);</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q0</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q1</span> <span class="special">=</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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q0</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q1</span> <span class="special">=</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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="special">};</span>
</pre>
<a name="boost_octonions.octonion_double"></a><p>
@@ -101,62 +101,62 @@
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">);</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q0</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q1</span> <span class="special">=</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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q0</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q1</span> <span class="special">=</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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="special">};</span>
</pre>
<a name="boost_octonions.octonion_long_double"></a><p>
@@ -167,62 +167,62 @@
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="identifier">value_type</span><span class="special">;</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">);</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q0</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q0</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="special">};</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespaces
@@ -230,7 +230,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -238,7 +238,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="template_class_octonion.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonion_member_typedefs.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="template_class_octonion.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.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="octonion_member_typedefs.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Octonion Value Operations</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" href="../../index.html" title="Boost.Octonions">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Boost.Octonions">
<link rel="up" href="../octonions.html" title="Octonions">
<link rel="prev" href="non_mem.html" title="Octonion Non-Member Operators">
<link rel="next" href="oct_create.html" title="Octonion Creation Functions">
@@ -20,16 +20,16 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="non_mem.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="oct_create.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="non_mem.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.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="oct_create.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_octonions.octonions.octonion_value_operations"></a><a href="octonion_value_operations.html" title="Octonion Value Operations">Octonion
<a name="boost_octonions.octonions.octonion_value_operations"></a><a class="link" href="octonion_value_operations.html" title="Octonion Value Operations">Octonion
Value Operations</a>
</h3></div></div></div>
<a name="boost_octonions.octonions.octonion_value_operations.real_and_unreal"></a><h5>
<a name="id542093"></a>
<a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.real_and_unreal">Real
<a name="id797506"></a>
<a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.real_and_unreal">Real
and Unreal</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">real</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
@@ -41,8 +41,8 @@
respectively.
</p>
<a name="boost_octonions.octonions.octonion_value_operations.conj"></a><h5>
<a name="id542373"></a>
<a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.conj">conj</a>
<a name="id797753"></a>
<a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.conj">conj</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
@@ -50,8 +50,8 @@
This returns the conjugate of the octonion.
</p>
<a name="boost_octonions.octonions.octonion_value_operations.sup"></a><h5>
<a name="id542512"></a>
<a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.sup">sup</a>
<a name="id797875"></a>
<a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.sup">sup</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">sup</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
@@ -59,8 +59,8 @@
This return the sup norm (the greatest among <code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())...</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">()))</span></code> of the octonion.
</p>
<a name="boost_octonions.octonions.octonion_value_operations.l1"></a><h5>
<a name="id542700"></a>
<a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.l1">l1</a>
<a name="id798041"></a>
<a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.l1">l1</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">l1</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
@@ -68,8 +68,8 @@
This return the l1 norm (<code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())+...+</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">o</span><span class="special">.</span><span class="identifier">R_component_8</span><span class="special">())</span></code>) of the octonion.
</p>
<a name="boost_octonions.octonions.octonion_value_operations.abs"></a><h5>
<a name="id542888"></a>
<a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.abs">abs</a>
<a name="id798208"></a>
<a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.abs">abs</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
@@ -77,8 +77,8 @@
This return the magnitude (Euclidian norm) of the octonion.
</p>
<a name="boost_octonions.octonions.octonion_value_operations.norm"></a><h5>
<a name="id543009"></a>
<a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.norm">norm</a>
<a name="id798316"></a>
<a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.norm">norm</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">norm</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span><span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
</pre>
@@ -92,7 +92,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -100,7 +100,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="non_mem.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="oct_create.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="non_mem.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.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="oct_create.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Octonions Transcendentals</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" href="../../index.html" title="Boost.Octonions">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Boost.Octonions">
<link rel="up" href="../octonions.html" title="Octonions">
<link rel="prev" href="oct_create.html" title="Octonion Creation Functions">
<link rel="next" href="test_program.html" title="Test Program">
@@ -20,11 +20,11 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="oct_create.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="test_program.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="oct_create.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.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="test_program.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_octonions.octonions.octonions_transcendentals"></a><a href="octonions_transcendentals.html" title="Octonions Transcendentals">Octonions
<a name="boost_octonions.octonions.octonions_transcendentals"></a><a class="link" href="octonions_transcendentals.html" title="Octonions Transcendentals">Octonions
Transcendentals</a>
</h3></div></div></div>
<p>
@@ -53,8 +53,8 @@
headers.
</p>
<a name="boost_octonions.octonions.octonions_transcendentals.exp"></a><h5>
<a name="id544327"></a>
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.exp">exp</a>
<a name="id799499"></a>
<a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.exp">exp</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
@@ -63,8 +63,8 @@
Computes the exponential of the octonion.
</p>
<a name="boost_octonions.octonions.octonions_transcendentals.cos"></a><h5>
<a name="id544464"></a>
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.cos">cos</a>
<a name="id799620"></a>
<a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.cos">cos</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">cos</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
@@ -73,8 +73,8 @@
Computes the cosine of the octonion
</p>
<a name="boost_octonions.octonions.octonions_transcendentals.sin"></a><h5>
<a name="id544601"></a>
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.sin">sin</a>
<a name="id799742"></a>
<a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.sin">sin</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
@@ -83,8 +83,8 @@
Computes the sine of the octonion.
</p>
<a name="boost_octonions.octonions.octonions_transcendentals.tan"></a><h5>
<a name="id544739"></a>
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.tan">tan</a>
<a name="id799864"></a>
<a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.tan">tan</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">tan</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
@@ -93,8 +93,8 @@
Computes the tangent of the octonion.
</p>
<a name="boost_octonions.octonions.octonions_transcendentals.cosh"></a><h5>
<a name="id544875"></a>
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.cosh">cosh</a>
<a name="id799985"></a>
<a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.cosh">cosh</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">cosh</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
@@ -103,8 +103,8 @@
Computes the hyperbolic cosine of the octonion.
</p>
<a name="boost_octonions.octonions.octonions_transcendentals.sinh"></a><h5>
<a name="id545014"></a>
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.sinh">sinh</a>
<a name="id800107"></a>
<a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.sinh">sinh</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">sinh</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
@@ -113,8 +113,8 @@
Computes the hyperbolic sine of the octonion.
</p>
<a name="boost_octonions.octonions.octonions_transcendentals.tanh"></a><h5>
<a name="id545152"></a>
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.tanh">tanh</a>
<a name="id800229"></a>
<a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.tanh">tanh</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">tanh</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
@@ -123,8 +123,8 @@
Computes the hyperbolic tangent of the octonion.
</p>
<a name="boost_octonions.octonions.octonions_transcendentals.pow"></a><h5>
<a name="id545292"></a>
<a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.pow">pow</a>
<a name="id800352"></a>
<a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.pow">pow</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n</span><span class="special">);</span>
@@ -135,7 +135,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -143,7 +143,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="oct_create.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="test_program.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="oct_create.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.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="test_program.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Overview</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" href="../../index.html" title="Boost.Octonions">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Boost.Octonions">
<link rel="up" href="../octonions.html" title="Octonions">
<link rel="prev" href="../octonions.html" title="Octonions">
<link rel="next" href="header_file.html" title="Header File">
@@ -20,11 +20,11 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../octonions.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="header_file.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="../octonions.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.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="header_file.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_octonions.octonions.overview"></a><a href="overview.html" title="Overview">Overview</a>
<a name="boost_octonions.octonions.overview"></a><a class="link" href="overview.html" title="Overview">Overview</a>
</h3></div></div></div>
<p>
Octonions, like <a href="../../../../quaternion/html/index.html" target="_top">quaternions</a>,
@@ -69,7 +69,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -77,7 +77,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../octonions.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="header_file.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="../octonions.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.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="header_file.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Synopsis</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" href="../../index.html" title="Boost.Octonions">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Boost.Octonions">
<link rel="up" href="../octonions.html" title="Octonions">
<link rel="prev" href="header_file.html" title="Header File">
<link rel="next" href="template_class_octonion.html" title="Template Class octonion">
@@ -20,111 +20,111 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="header_file.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="template_class_octonion.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="header_file.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.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="template_class_octonion.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_octonions.octonions.synopsis"></a><a href="synopsis.html" title="Synopsis">Synopsis</a>
<a name="boost_octonions.octonions.synopsis"></a><a class="link" href="synopsis.html" title="Synopsis">Synopsis</a>
</h3></div></div></div>
<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">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">class</span> <a href="template_class_octonion.html" title="Template Class octonion">octonion</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">class</span> <a href="octonion_specializations.html" title="Octonion Specializations">octonion&lt;float&gt;</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">class</span> <a href="octonion_specializations.html#boost_octonions.octonion_double">octonion&lt;double&gt;</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">class</span> <a href="octonion_specializations.html#boost_octonions.octonion_long_double">octonion&lt;long double&gt;</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">class</span> <a class="link" href="template_class_octonion.html" title="Template Class octonion">octonion</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">class</span> <a class="link" href="octonion_specializations.html" title="Octonion Specializations">octonion&lt;float&gt;</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">class</span> <a class="link" href="octonion_specializations.html#boost_octonions.octonion_double">octonion&lt;double&gt;</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">class</span> <a class="link" href="octonion_specializations.html#boost_octonions.octonion_long_double">octonion&lt;long double&gt;</a><span class="special">;</span>
<span class="comment">// operators
</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.unary_plus_and_minus_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.unary_plus_and_minus_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.unary_plus_and_minus_operators">operator +</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.unary_plus_and_minus_operators">operator -</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.binary_inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.stream_extractor">operator &gt;&gt;</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">is</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.stream_extractor">operator &gt;&gt;</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">is</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="non_mem.html#boost_octonions.octonions.non_mem.stream_inserter">operator &lt;&lt;</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">os</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="non_mem.html#boost_octonions.octonions.non_mem.stream_inserter">operator &lt;&lt;</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">os</span><span class="special">,</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="comment">// values
</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.real_and_unreal">real</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.real_and_unreal">unreal</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.real_and_unreal">real</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.real_and_unreal">unreal</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.sup">sup</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.l1">l1</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span><span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.abs">abs</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.norm">norm</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span><span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.conj">conj</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.sup">sup</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.l1">l1</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span><span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.abs">abs</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.norm">norm</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span><span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonion_value_operations.html#boost_octonions.octonions.octonion_value_operations.conj">conj</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="oct_create.html" title="Octonion Creation Functions">spherical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi6</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="oct_create.html" title="Octonion Creation Functions">multipolar</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta4</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="oct_create.html" title="Octonion Creation Functions">cylindrical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">angle</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h6</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="oct_create.html" title="Octonion Creation Functions">spherical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi6</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="oct_create.html" title="Octonion Creation Functions">multipolar</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta4</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="oct_create.html" title="Octonion Creation Functions">cylindrical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">angle</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h3</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h4</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h5</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h6</span><span class="special">);</span>
<span class="comment">// transcendentals
</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.exp">exp</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.cos">cos</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.sin">sin</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.tan">tan</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.cosh">cosh</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.sinh">sinh</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.tanh">tanh</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.exp">exp</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.cos">cos</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.sin">sin</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.tan">tan</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.cosh">cosh</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.sinh">sinh</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.tanh">tanh</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.pow">pow</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonions_transcendentals.html#boost_octonions.octonions.octonions_transcendentals.pow">pow</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">o</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n</span><span class="special">);</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespaces
</span></pre>
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -132,7 +132,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="header_file.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="template_class_octonion.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Template Class octonion</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
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@@ -20,11 +20,11 @@
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<div class="spirit-nav">
<a accesskey="p" href="synopsis.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../octonions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="octonion_specializations.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_octonions.octonions.template_class_octonion"></a><a href="template_class_octonion.html" title="Template Class octonion">Template
<a name="boost_octonions.octonions.template_class_octonion"></a><a class="link" href="template_class_octonion.html" title="Template Class octonion">Template
Class octonion</a>
</h3></div></div></div>
<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>
@@ -35,62 +35,62 @@
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="identifier">T</span> <span class="identifier">value_type</span><span class="special">;</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">());</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q0</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q1</span> <span class="special">=</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_e</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_f</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_g</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_h</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">());</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z2</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;(),</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z3</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q0</span><span class="special">,</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q1</span> <span class="special">=</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;());</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="keyword">explicit</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.constructors">octonion</a><span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_5</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_6</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_7</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_real_components">R_component_8</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_complex_components">C_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.individual_quaternion_components">H_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.assignment_operators">operator =</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator +=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator -=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator *=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <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">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <a class="link" href="octonion_member_functions.html#boost_octonions.octonions.octonion_member_functions.other_member_operators">operator /=</a> <span class="special">(</span><span class="identifier">octonion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="special">};</span>
<span class="special">}</span> <span class="special">}</span> <span class="comment">// namespaces
@@ -98,7 +98,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -106,7 +106,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
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<p>
The <a href="../../../../../octonion/octonion_test.cpp" target="_top">octonion_test.cpp</a>
@@ -44,7 +44,7 @@
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@@ -52,7 +52,7 @@
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Improve testing.
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Improve testing.
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Put in place an Expression Template mechanism (perhaps borrowing from
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -47,7 +48,7 @@
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<dt><span class="section"><a href="quaternions/overview.html">Overview</a></span></dt>
@@ -53,7 +53,7 @@
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<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 © 2001 -2003 Hubert Holin<p>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -61,7 +61,7 @@
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<p>
The mathematical text has been typeset with <a href="http://www.nisus-soft.com/" target="_top">Nisus
@@ -36,7 +36,7 @@
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<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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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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<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">spherical</span><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi2</span><span class="special">);</span>
@@ -102,7 +102,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -110,7 +110,7 @@
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@@ -20,26 +20,30 @@
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<a name="boost_quaternions.quaternions.exp"></a><a href="exp.html" title="The Quaternionic Exponential"> The Quaternionic
<a name="boost_quaternions.quaternions.exp"></a><a class="link" href="exp.html" title="The Quaternionic Exponential"> The Quaternionic
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<p>
Please refer to the following PDF's:
</p>
<div class="itemizedlist"><ul type="disc">
<li><a href="../../../../../quaternion/TQE.pdf" target="_top">The Quaternionic Exponential (and
beyond)</a></li>
<li><a href="../../../../../quaternion/TQE_EA.pdf" target="_top">The Quaternionic Exponential
(and beyond) ERRATA &amp; ADDENDA</a></li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a href="../../../../../quaternion/TQE.pdf" target="_top">The Quaternionic Exponential
(and beyond)</a>
</li>
<li class="listitem">
<a href="../../../../../quaternion/TQE_EA.pdf" target="_top">The Quaternionic Exponential
(and beyond) ERRATA &amp; ADDENDA</a>
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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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@@ -47,7 +51,7 @@
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<html>
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<p>
The interface and implementation are both supplied by the header file <a href="../../../../../../../boost/math/quaternion.hpp" target="_top">quaternion.hpp</a>.
@@ -32,7 +32,7 @@
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -40,7 +40,7 @@
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@@ -20,80 +20,82 @@
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<a name="boost_quaternions.quaternions.history"></a><a href="history.html" title="History">History</a>
<a name="boost_quaternions.quaternions.history"></a><a class="link" href="history.html" title="History">History</a>
</h3></div></div></div>
<div class="itemizedlist"><ul type="disc">
<li>
1.5.8 - 17/12/2005: Converted documentation to Quickbook Format.
</li>
<li>
1.5.7 - 24/02/2003: transitionned to the unit test framework; &lt;boost/config.hpp&gt;
now included by the library header (rather than the test files).
</li>
<li>
1.5.6 - 15/10/2002: Gcc2.95.x and stlport on linux compatibility by Alkis
Evlogimenos (alkis@routescience.com).
</li>
<li>
1.5.5 - 27/09/2002: Microsoft VCPP 7 compatibility, by Michael Stevens
(michael@acfr.usyd.edu.au); requires the /Za compiler option.
</li>
<li>
1.5.4 - 19/09/2002: fixed problem with multiple inclusion (in different
translation units); attempt at an improved compatibility with Microsoft
compilers, by Michael Stevens (michael@acfr.usyd.edu.au) and Fredrik Blomqvist;
other compatibility fixes.
</li>
<li>
1.5.3 - 01/02/2002: bugfix and Gcc 2.95.3 compatibility by Douglas Gregor
(gregod@cs.rpi.edu).
</li>
<li>
1.5.2 - 07/07/2001: introduced namespace math.
</li>
<li>
1.5.1 - 07/06/2001: (end of Boost review) now includes &lt;boost/math/special_functions/sinc.hpp&gt;
and &lt;boost/math/special_functions/sinhc.hpp&gt; instead of &lt;boost/special_functions.hpp&gt;;
corrected bug in sin (Daryle Walker); removed check for self-assignment
(Gary Powel); made converting functions explicit (Gary Powel); added overflow
guards for division operators and abs (Peter Schmitteckert); added sup
and l1; used Vesa Karvonen's CPP metaprograming technique to simplify code.
</li>
<li>
1.5.0 - 26/03/2001: boostification, inlining of all operators except input,
output and pow, fixed exception safety of some members (template version)
and output operator, added spherical, semipolar, multipolar, cylindrospherical
and cylindrical.
</li>
<li>
1.4.0 - 09/01/2001: added tan and tanh.
</li>
<li>
1.3.1 - 08/01/2001: cosmetic fixes.
</li>
<li>
1.3.0 - 12/07/2000: pow now uses Maarten Hilferink's (mhilferink@tip.nl)
algorithm.
</li>
<li>
1.2.0 - 25/05/2000: fixed the division operators and output; changed many
signatures.
</li>
<li>
1.1.0 - 23/05/2000: changed sinc into sinc_pi; added sin, cos, sinh, cosh.
</li>
<li>
1.0.0 - 10/08/1999: first public version.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
1.5.8 - 17/12/2005: Converted documentation to Quickbook Format.
</li>
<li class="listitem">
1.5.7 - 24/02/2003: transitionned to the unit test framework; &lt;boost/config.hpp&gt;
now included by the library header (rather than the test files).
</li>
<li class="listitem">
1.5.6 - 15/10/2002: Gcc2.95.x and stlport on linux compatibility by Alkis
Evlogimenos (alkis@routescience.com).
</li>
<li class="listitem">
1.5.5 - 27/09/2002: Microsoft VCPP 7 compatibility, by Michael Stevens
(michael@acfr.usyd.edu.au); requires the /Za compiler option.
</li>
<li class="listitem">
1.5.4 - 19/09/2002: fixed problem with multiple inclusion (in different
translation units); attempt at an improved compatibility with Microsoft
compilers, by Michael Stevens (michael@acfr.usyd.edu.au) and Fredrik
Blomqvist; other compatibility fixes.
</li>
<li class="listitem">
1.5.3 - 01/02/2002: bugfix and Gcc 2.95.3 compatibility by Douglas Gregor
(gregod@cs.rpi.edu).
</li>
<li class="listitem">
1.5.2 - 07/07/2001: introduced namespace math.
</li>
<li class="listitem">
1.5.1 - 07/06/2001: (end of Boost review) now includes &lt;boost/math/special_functions/sinc.hpp&gt;
and &lt;boost/math/special_functions/sinhc.hpp&gt; instead of &lt;boost/special_functions.hpp&gt;;
corrected bug in sin (Daryle Walker); removed check for self-assignment
(Gary Powel); made converting functions explicit (Gary Powel); added
overflow guards for division operators and abs (Peter Schmitteckert);
added sup and l1; used Vesa Karvonen's CPP metaprograming technique to
simplify code.
</li>
<li class="listitem">
1.5.0 - 26/03/2001: boostification, inlining of all operators except
input, output and pow, fixed exception safety of some members (template
version) and output operator, added spherical, semipolar, multipolar,
cylindrospherical and cylindrical.
</li>
<li class="listitem">
1.4.0 - 09/01/2001: added tan and tanh.
</li>
<li class="listitem">
1.3.1 - 08/01/2001: cosmetic fixes.
</li>
<li class="listitem">
1.3.0 - 12/07/2000: pow now uses Maarten Hilferink's (mhilferink@tip.nl)
algorithm.
</li>
<li class="listitem">
1.2.0 - 25/05/2000: fixed the division operators and output; changed
many signatures.
</li>
<li class="listitem">
1.1.0 - 23/05/2000: changed sinc into sinc_pi; added sin, cos, sinh,
cosh.
</li>
<li class="listitem">
1.0.0 - 10/08/1999: first public version.
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -101,7 +103,7 @@
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<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
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@@ -20,16 +20,16 @@
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<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_quaternions.quaternions.mem_fun"></a><a href="mem_fun.html" title="Quaternion Member Functions"> Quaternion Member
<a name="boost_quaternions.quaternions.mem_fun"></a><a class="link" href="mem_fun.html" title="Quaternion Member Functions"> Quaternion Member
Functions</a>
</h3></div></div></div>
<a name="boost_quaternions.quaternions.mem_fun.constructors"></a><h4>
<a name="id516686"></a>
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">Constructors</a>
<a name="id774790"></a>
<a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">Constructors</a>
</h4>
<p>
Template version:
@@ -80,13 +80,13 @@
function in a "detail" subnamespace.
</p>
<a name="boost_quaternions.quaternions.mem_fun.other_member_functions"></a><h4>
<a name="id518710"></a>
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.other_member_functions">Other
<a name="id776568"></a>
<a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.other_member_functions">Other
member functions</a>
</h4>
<a name="boost_quaternions.quaternions.mem_fun.real_and_unreal_parts"></a><h5>
<a name="id518734"></a>
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">Real
<a name="id776589"></a>
<a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">Real
and Unreal Parts</a>
</h5>
<pre class="programlisting"><span class="identifier">T</span> <span class="identifier">real</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
@@ -100,8 +100,8 @@
case). These are returned by the first two functions.
</p>
<a name="boost_quaternions.quaternions.mem_fun.individual_real_components"></a><h5>
<a name="id518840"></a>
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">Individual
<a name="id776691"></a>
<a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">Individual
Real Components</a>
</h5>
<pre class="programlisting"><span class="identifier">T</span> <span class="identifier">R_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
@@ -114,8 +114,8 @@
functions. Hence real and R_component_1 return the same value.
</p>
<a name="boost_quaternions.quaternions.mem_fun.individual_complex__components"></a><h5>
<a name="id518989"></a>
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">Individual
<a name="id776825"></a>
<a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">Individual
Complex Components</a>
</h5>
<pre class="programlisting"><span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">C_component_1</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
@@ -129,13 +129,13 @@
is the same as <code class="computeroutput"><span class="identifier">q</span><span class="special">.</span><span class="identifier">real</span><span class="special">()</span></code>.
</p>
<a name="boost_quaternions.quaternions.mem_fun.quaternion_member_operators"></a><h4>
<a name="id519212"></a>
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.quaternion_member_operators">Quaternion
<a name="id777024"></a>
<a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.quaternion_member_operators">Quaternion
Member Operators</a>
</h4>
<a name="boost_quaternions.quaternions.mem_fun.assignment_operators"></a><h5>
<a name="id519237"></a>
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">Assignment
<a name="id777032"></a>
<a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">Assignment
Operators</a>
</h5>
<pre class="programlisting"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
@@ -151,8 +151,8 @@
base type's assignment operators must not throw.
</p>
<a name="boost_quaternions.quaternions.mem_fun.addition_operators"></a><h5>
<a name="id519625"></a>
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">Addition
<a name="id777393"></a>
<a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">Addition
Operators</a>
</h5>
<pre class="programlisting"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">+=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span>
@@ -168,8 +168,8 @@
base type's assignment operators must not throw.
</p>
<a name="boost_quaternions.quaternions.mem_fun.subtraction_operators"></a><h5>
<a name="id519981"></a>
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">Subtraction
<a name="id777707"></a>
<a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">Subtraction
Operators</a>
</h5>
<pre class="programlisting"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">-=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span>
@@ -185,8 +185,8 @@
base type's assignment operators must not throw.
</p>
<a name="boost_quaternions.quaternions.mem_fun.multiplication_operators"></a><h5>
<a name="id520336"></a>
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">Multiplication
<a name="id778022"></a>
<a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">Multiplication
Operators</a>
</h5>
<pre class="programlisting"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">*=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span>
@@ -203,8 +203,8 @@
assignment operators must not throw.
</p>
<a name="boost_quaternions.quaternions.mem_fun.division_operators"></a><h5>
<a name="id520696"></a>
<a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">Division
<a name="id778343"></a>
<a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">Division
Operators</a>
</h5>
<pre class="programlisting"><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <span class="special">/=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">)</span>
@@ -223,7 +223,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -231,7 +231,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="mem_typedef.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="non_mem.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="mem_typedef.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.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="non_mem.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
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View File

@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Quaternion Member Typedefs</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" href="../../index.html" title="Boost.Quaternions">
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<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
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<link rel="next" href="mem_fun.html" title="Quaternion Member Functions">
@@ -20,11 +20,11 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="spec.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="mem_fun.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="spec.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.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="mem_fun.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
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<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_quaternions.quaternions.mem_typedef"></a><a href="mem_typedef.html" title="Quaternion Member Typedefs"> Quaternion
<a name="boost_quaternions.quaternions.mem_typedef"></a><a class="link" href="mem_typedef.html" title="Quaternion Member Typedefs"> Quaternion
Member Typedefs</a>
</h3></div></div></div>
<p>
@@ -56,7 +56,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -64,7 +64,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="spec.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="mem_fun.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="spec.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.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="mem_fun.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
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View File

@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Quaternion Non-Member Operators</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" href="../../index.html" title="Boost.Quaternions">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Boost.Quaternions">
<link rel="up" href="../quaternions.html" title="Quaternions">
<link rel="prev" href="mem_fun.html" title="Quaternion Member Functions">
<link rel="next" href="value_op.html" title="Quaternion Value Operations">
@@ -20,16 +20,16 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="mem_fun.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="value_op.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="mem_fun.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.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="value_op.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_quaternions.quaternions.non_mem"></a><a href="non_mem.html" title="Quaternion Non-Member Operators"> Quaternion Non-Member
<a name="boost_quaternions.quaternions.non_mem"></a><a class="link" href="non_mem.html" title="Quaternion Non-Member Operators"> Quaternion Non-Member
Operators</a>
</h3></div></div></div>
<a name="boost_quaternions.quaternions.non_mem.unary_plus"></a><h5>
<a name="id521094"></a>
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_plus">Unary Plus</a>
<a name="id778695"></a>
<a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_plus">Unary Plus</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
@@ -38,8 +38,8 @@
This unary operator simply returns q.
</p>
<a name="boost_quaternions.quaternions.non_mem.unary_minus"></a><h5>
<a name="id521239"></a>
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_minus">Unary Minus</a>
<a name="id778824"></a>
<a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_minus">Unary Minus</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
@@ -48,8 +48,8 @@
This unary operator returns the opposite of q.
</p>
<a name="boost_quaternions.quaternions.non_mem.binary_addition_operators"></a><h5>
<a name="id521385"></a>
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">Binary
<a name="id778952"></a>
<a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">Binary
Addition Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">+</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
@@ -63,8 +63,8 @@
<span class="identifier">rhs</span></code>.
</p>
<a name="boost_quaternions.quaternions.non_mem.binary_subtraction_operators"></a><h5>
<a name="id522245"></a>
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">Binary
<a name="id779712"></a>
<a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">Binary
Subtraction Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">-</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
@@ -78,8 +78,8 @@
<span class="identifier">rhs</span></code>.
</p>
<a name="boost_quaternions.quaternions.non_mem.binary_multiplication_operators"></a><h5>
<a name="id523106"></a>
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">Binary
<a name="id780472"></a>
<a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">Binary
Multiplication Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
@@ -93,8 +93,8 @@
<span class="identifier">rhs</span></code>.
</p>
<a name="boost_quaternions.quaternions.non_mem.binary_division_operators"></a><h5>
<a name="id523967"></a>
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">Binary
<a name="id781229"></a>
<a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">Binary
Division Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">operator</span> <span class="special">/</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
@@ -109,8 +109,8 @@
to divide by zero...
</p>
<a name="boost_quaternions.quaternions.non_mem.equality_operators"></a><h5>
<a name="id524827"></a>
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">Equality
<a name="id781988"></a>
<a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">Equality
Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">==</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
@@ -125,8 +125,8 @@
with any floating-type entity, this is essentially meaningless.
</p>
<a name="boost_quaternions.quaternions.non_mem.inequality_operators"></a><h5>
<a name="id525637"></a>
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">Inequality
<a name="id782704"></a>
<a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">Inequality
Operators</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <span class="keyword">operator</span> <span class="special">!=</span> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
@@ -141,8 +141,8 @@
false. As with any floating-type entity, this is essentially meaningless.
</p>
<a name="boost_quaternions.quaternions.non_mem.stream_extractor"></a><h5>
<a name="id526447"></a>
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_extractor">Stream
<a name="id783419"></a>
<a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_extractor">Stream
Extractor</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
@@ -173,8 +173,8 @@
complex numbers which happen to have imaginary parts equal to zero).
</p>
<a name="boost_quaternions.quaternions.non_mem.stream_inserter"></a><h5>
<a name="id526824"></a>
<a href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_inserter">Stream
<a name="id783748"></a>
<a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_inserter">Stream
Inserter</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
@@ -206,7 +206,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -214,7 +214,7 @@
</tr></table>
<hr>
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<a accesskey="p" href="mem_fun.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="value_op.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Overview</title>
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<p>
Quaternions are a relative of complex numbers.
@@ -79,7 +79,7 @@
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<a name="boost_quaternions.quaternions.quat"></a><a href="quat.html" title="Template Class quaternion"> Template Class quaternion</a>
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<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>
@@ -33,47 +33,47 @@
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="identifier">T</span> <a href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
<span class="keyword">typedef</span> <span class="identifier">T</span> <a class="link" href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">());</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">(),</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="identifier">T</span><span class="special">());</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;());</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="identifier">T</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">T</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="special">};</span>
<span class="special">}</span> <span class="comment">// namespace math
@@ -82,7 +82,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -90,7 +90,7 @@
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@@ -1,10 +1,10 @@
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<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Quaternion Specializations</title>
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<a name="boost_quaternions.quaternions.spec"></a><a href="spec.html" title="Quaternion Specializations"> Quaternion Specializations</a>
<a name="boost_quaternions.quaternions.spec"></a><a class="link" href="spec.html" title="Quaternion Specializations"> Quaternion Specializations</a>
</h3></div></div></div>
<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>
@@ -32,47 +32,47 @@
<span class="keyword">class</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="keyword">float</span> <a href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">float</span> <a class="link" href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">);</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">,</span> <span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0f</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">float</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">float</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="keyword">float</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="special">};</span>
</pre>
<a name="boost_quaternions.quaternion_double"></a><p>
@@ -81,47 +81,47 @@
<span class="keyword">class</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="keyword">double</span> <a href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">double</span> <a class="link" href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">);</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">,</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">double</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="special">};</span>
</pre>
<a name="boost_quaternions.quaternion_long_double"></a><p>
@@ -130,47 +130,47 @@
<span class="keyword">class</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span>
<span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
<span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">double</span> <a href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
<span class="keyword">typedef</span> <span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="mem_typedef.html" title="Quaternion Member Typedefs">value_type</a><span class="special">;</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">);</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_a</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_b</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_c</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">,</span> <span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">requested_d</span> <span class="special">=</span> <span class="number">0.0L</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z0</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">z1</span> <span class="special">=</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;());</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">explicit</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.constructors">quaternion</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_recopier</span><span class="special">);</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">real</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.real_and_unreal_parts">unreal</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_3</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="keyword">long</span> <span class="keyword">double</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_real_components">R_component_4</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_1</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.individual_complex__components">C_component_2</a><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.assignment_operators">operator = </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">a_affecter</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.addition_operators">operator += </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.subtraction_operators">operator -= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.multiplication_operators">operator *= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="keyword">long</span> <span class="keyword">double</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">X</span><span class="special">&gt;</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="identifier">quaternion</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;&amp;</span> <a class="link" href="mem_fun.html#boost_quaternions.quaternions.mem_fun.division_operators">operator /= </a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">X</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="special">};</span>
<span class="special">}</span> <span class="comment">// namespace math
@@ -179,7 +179,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -187,7 +187,7 @@
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<title>Synopsis</title>
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<a name="boost_quaternions.quaternions.synopsis"></a><a href="synopsis.html" title="Synopsis">Synopsis</a>
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<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">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">class</span> <a href="quat.html" title="Template Class quaternion">quaternion</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">class</span> <a href="spec.html" title="Quaternion Specializations">quaternion&lt;float&gt;</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">class</span> <a href="spec.html#boost_quaternions.quaternion_double">quaternion&lt;double&gt;</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">class</span> <a href="spec.html#boost_quaternions.quaternion_long_double">quaternion&lt;long double&gt;</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">class</span> <a class="link" href="quat.html" title="Template Class quaternion">quaternion</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">class</span> <a class="link" href="spec.html" title="Quaternion Specializations">quaternion&lt;float&gt;</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">class</span> <a class="link" href="spec.html#boost_quaternions.quaternion_double">quaternion&lt;double&gt;</a><span class="special">;</span>
<span class="keyword">template</span><span class="special">&lt;&gt;</span> <span class="keyword">class</span> <a class="link" href="spec.html#boost_quaternions.quaternion_long_double">quaternion&lt;long double&gt;</a><span class="special">;</span>
<span class="comment">// operators
</span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
</span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_addition_operators">operator +</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_subtraction_operators">operator -</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_multiplication_operators">operator *</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.binary_division_operators">operator /</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_plus">operator +</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_minus">operator -</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_plus">operator +</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.unary_minus">operator -</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.equality_operators">operator ==</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">bool</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.inequality_operators">operator !=</a> <span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">lhs</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rhs</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;&amp;</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_extractor">operator &gt;&gt;</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">is</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;&amp;</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_extractor">operator &gt;&gt;</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">is</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">charT</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">traits</span><span class="special">&gt;</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <a href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_inserter">operator &lt;&lt;</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">os</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="special">::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;&amp;</span> <span class="keyword">operator</span> <a class="link" href="non_mem.html#boost_quaternions.quaternions.non_mem.stream_inserter">operator &lt;&lt;</a> <span class="special">(::</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span><span class="identifier">charT</span><span class="special">,</span><span class="identifier">traits</span><span class="special">&gt;</span> <span class="special">&amp;</span> <span class="identifier">os</span><span class="special">,</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="comment">// values
</span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a href="value_op.html#boost_quaternions.quaternions.value_op.real_and_unreal">real</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="value_op.html#boost_quaternions.quaternions.value_op.real_and_unreal">unreal</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
</span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.real_and_unreal">real</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.real_and_unreal">unreal</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a href="value_op.html#boost_quaternions.quaternions.value_op.sup">sup</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a href="value_op.html#boost_quaternions.quaternions.value_op.l1">l1</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a href="value_op.html#boost_quaternions.quaternions.value_op.abs">abs</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a href="value_op.html#boost_quaternions.quaternions.value_op.norm">norm</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span><span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="value_op.html#boost_quaternions.quaternions.value_op.conj">conj</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.sup">sup</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.l1">l1</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.abs">abs</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.norm">norm</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span><span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.conj">conj</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="create.html#boost_quaternions.quaternions.creation_spherical">spherical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi2</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="create.html#boost_quaternions.quaternions.creation_semipolar">semipolar</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta2</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="create.html#boost_quaternions.quaternions.creation_multipolar">multipolar</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta2</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="create.html#boost_quaternions.quaternions.creation_cylindrospherical">cylindrospherical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">radius</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">longitude</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">latitude</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="create.html#boost_quaternions.quaternions.creation_cylindrical">cylindrical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">angle</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h2</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="create.html#boost_quaternions.quaternions.creation_spherical">spherical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">phi2</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="create.html#boost_quaternions.quaternions.creation_semipolar">semipolar</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta2</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="create.html#boost_quaternions.quaternions.creation_multipolar">multipolar</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">rho2</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">theta2</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="create.html#boost_quaternions.quaternions.creation_cylindrospherical">cylindrospherical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">t</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">radius</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">longitude</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">latitude</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="create.html#boost_quaternions.quaternions.creation_cylindrical">cylindrical</a><span class="special">(</span><span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">angle</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h1</span><span class="special">,</span> <span class="identifier">T</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">h2</span><span class="special">);</span>
<span class="comment">// transcendentals
</span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="trans.html#boost_quaternions.quaternions.trans.exp">exp</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="trans.html#boost_quaternions.quaternions.trans.cos">cos</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="trans.html#boost_quaternions.quaternions.trans.sin">sin</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="trans.html#boost_quaternions.quaternions.trans.tan">tan</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="trans.html#boost_quaternions.quaternions.trans.cosh">cosh</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="trans.html#boost_quaternions.quaternions.trans.sinh">sinh</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="trans.html#boost_quaternions.quaternions.trans.tanh">tanh</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a href="trans.html#boost_quaternions.quaternions.trans.pow">pow</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n</span><span class="special">);</span>
</span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="trans.html#boost_quaternions.quaternions.trans.exp">exp</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="trans.html#boost_quaternions.quaternions.trans.cos">cos</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="trans.html#boost_quaternions.quaternions.trans.sin">sin</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="trans.html#boost_quaternions.quaternions.trans.tan">tan</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="trans.html#boost_quaternions.quaternions.trans.cosh">cosh</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="trans.html#boost_quaternions.quaternions.trans.sinh">sinh</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="trans.html#boost_quaternions.quaternions.trans.tanh">tanh</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
<span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <a class="link" href="trans.html#boost_quaternions.quaternions.trans.pow">pow</a><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n</span><span class="special">);</span>
<span class="special">}</span> <span class="comment">// namespace math
</span><span class="special">}</span> <span class="comment">// namespace boost
@@ -111,7 +111,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -119,7 +119,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="header_file.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="quat.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="header_file.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.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="quat.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Test Program</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" href="../../index.html" title="Boost.Quaternions">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Boost.Quaternions">
<link rel="up" href="../quaternions.html" title="Quaternions">
<link rel="prev" href="trans.html" title="Quaternion Transcendentals">
<link rel="next" href="exp.html" title="The Quaternionic Exponential">
@@ -20,11 +20,11 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="trans.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="exp.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="trans.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.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="exp.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_quaternions.quaternions.test_program"></a><a href="test_program.html" title="Test Program">Test Program</a>
<a name="boost_quaternions.quaternions.test_program"></a><a class="link" href="test_program.html" title="Test Program">Test Program</a>
</h3></div></div></div>
<p>
The <a href="../../../../../quaternion/quaternion_test.cpp" target="_top">quaternion_test.cpp</a>
@@ -45,7 +45,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -53,7 +53,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="trans.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="exp.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="trans.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.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="exp.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>To Do</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" href="../../index.html" title="Boost.Quaternions">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Boost.Quaternions">
<link rel="up" href="../quaternions.html" title="Quaternions">
<link rel="prev" href="history.html" title="History">
</head>
@@ -19,31 +19,32 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="history.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a>
<a accesskey="p" href="history.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.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>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_quaternions.quaternions.to_do"></a><a href="to_do.html" title="To Do">To Do</a>
<a name="boost_quaternions.quaternions.to_do"></a><a class="link" href="to_do.html" title="To Do">To Do</a>
</h3></div></div></div>
<div class="itemizedlist"><ul type="disc">
<li>
Improve testing.
</li>
<li>
Rewrite input operatore using Spirit (creates a dependency).
</li>
<li>
Put in place an Expression Template mechanism (perhaps borrowing from uBlas).
</li>
<li>
Use uBlas for the link with rotations (and move from the <a href="../../../../../quaternion/HSO3SO4.cpp" target="_top">example</a>
implementation to an efficient one).
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Improve testing.
</li>
<li class="listitem">
Rewrite input operatore using Spirit (creates a dependency).
</li>
<li class="listitem">
Put in place an Expression Template mechanism (perhaps borrowing from
uBlas).
</li>
<li class="listitem">
Use uBlas for the link with rotations (and move from the <a href="../../../../../quaternion/HSO3SO4.cpp" target="_top">example</a>
implementation to an efficient one).
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -51,7 +52,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="history.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a>
<a accesskey="p" href="history.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.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>
</div>
</body>
</html>

View File

@@ -1,10 +1,10 @@
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1">
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Quaternion Transcendentals</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets Vsnapshot_2006-12-17_0120">
<link rel="start" href="../../index.html" title="Boost.Quaternions">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Boost.Quaternions">
<link rel="up" href="../quaternions.html" title="Quaternions">
<link rel="prev" href="create.html" title="Quaternion Creation Functions">
<link rel="next" href="test_program.html" title="Test Program">
@@ -20,11 +20,11 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="create.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="test_program.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="create.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../quaternions.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="test_program.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_quaternions.quaternions.trans"></a><a href="trans.html" title="Quaternion Transcendentals"> Quaternion Transcendentals</a>
<a name="boost_quaternions.quaternions.trans"></a><a class="link" href="trans.html" title="Quaternion Transcendentals"> Quaternion Transcendentals</a>
</h3></div></div></div>
<p>
There is no <code class="computeroutput"><span class="identifier">log</span></code> or <code class="computeroutput"><span class="identifier">sqrt</span></code> provided for quaternions in this implementation,
@@ -56,8 +56,8 @@
headers.
</p>
<a name="boost_quaternions.quaternions.trans.exp"></a><h5>
<a name="id530581"></a>
<a href="trans.html#boost_quaternions.quaternions.trans.exp">exp</a>
<a name="id787126"></a>
<a class="link" href="trans.html#boost_quaternions.quaternions.trans.exp">exp</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">exp</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
</pre>
@@ -65,8 +65,8 @@
Computes the exponential of the quaternion.
</p>
<a name="boost_quaternions.quaternions.trans.cos"></a><h5>
<a name="id445584"></a>
<a href="trans.html#boost_quaternions.quaternions.trans.cos">cos</a>
<a name="id787246"></a>
<a class="link" href="trans.html#boost_quaternions.quaternions.trans.cos">cos</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">cos</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
</pre>
@@ -74,8 +74,8 @@
Computes the cosine of the quaternion
</p>
<a name="boost_quaternions.quaternions.trans.sin"></a><h5>
<a name="id530717"></a>
<a href="trans.html#boost_quaternions.quaternions.trans.sin">sin</a>
<a name="id787367"></a>
<a class="link" href="trans.html#boost_quaternions.quaternions.trans.sin">sin</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">sin</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
</pre>
@@ -83,8 +83,8 @@
Computes the sine of the quaternion.
</p>
<a name="boost_quaternions.quaternions.trans.tan"></a><h5>
<a name="id530853"></a>
<a href="trans.html#boost_quaternions.quaternions.trans.tan">tan</a>
<a name="id787487"></a>
<a class="link" href="trans.html#boost_quaternions.quaternions.trans.tan">tan</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">tan</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
</pre>
@@ -92,8 +92,8 @@
Computes the tangent of the quaternion.
</p>
<a name="boost_quaternions.quaternions.trans.cosh"></a><h5>
<a name="id530991"></a>
<a href="trans.html#boost_quaternions.quaternions.trans.cosh">cosh</a>
<a name="id787608"></a>
<a class="link" href="trans.html#boost_quaternions.quaternions.trans.cosh">cosh</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">cosh</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
</pre>
@@ -101,8 +101,8 @@
Computes the hyperbolic cosine of the quaternion.
</p>
<a name="boost_quaternions.quaternions.trans.sinh"></a><h5>
<a name="id531129"></a>
<a href="trans.html#boost_quaternions.quaternions.trans.sinh">sinh</a>
<a name="id787730"></a>
<a class="link" href="trans.html#boost_quaternions.quaternions.trans.sinh">sinh</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">sinh</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
</pre>
@@ -110,8 +110,8 @@
Computes the hyperbolic sine of the quaternion.
</p>
<a name="boost_quaternions.quaternions.trans.tanh"></a><h5>
<a name="id531266"></a>
<a href="trans.html#boost_quaternions.quaternions.trans.tanh">tanh</a>
<a name="id787851"></a>
<a class="link" href="trans.html#boost_quaternions.quaternions.trans.tanh">tanh</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">tanh</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
</pre>
@@ -119,8 +119,8 @@
Computes the hyperbolic tangent of the quaternion.
</p>
<a name="boost_quaternions.quaternions.trans.pow"></a><h5>
<a name="id531403"></a>
<a href="trans.html#boost_quaternions.quaternions.trans.pow">pow</a>
<a name="id787972"></a>
<a class="link" href="trans.html#boost_quaternions.quaternions.trans.pow">pow</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">pow</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">,</span> <span class="keyword">int</span> <span class="identifier">n</span><span class="special">);</span>
</pre>
@@ -130,7 +130,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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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@@ -138,7 +138,7 @@
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<a name="boost_quaternions.quaternions.value_op"></a><a href="value_op.html" title="Quaternion Value Operations"> Quaternion Value
<a name="boost_quaternions.quaternions.value_op"></a><a class="link" href="value_op.html" title="Quaternion Value Operations"> Quaternion Value
Operations</a>
</h3></div></div></div>
<a name="boost_quaternions.quaternions.value_op.real_and_unreal"></a><h5>
<a name="id527777"></a>
<a href="value_op.html#boost_quaternions.quaternions.value_op.real_and_unreal">real
<a name="id784593"></a>
<a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.real_and_unreal">real
and unreal</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">real</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
@@ -41,8 +41,8 @@
respectively.
</p>
<a name="boost_quaternions.quaternions.value_op.conj"></a><h5>
<a name="id528058"></a>
<a href="value_op.html#boost_quaternions.quaternions.value_op.conj">conj</a>
<a name="id784840"></a>
<a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.conj">conj</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">conj</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
</pre>
@@ -50,8 +50,8 @@
This returns the conjugate of the quaternion.
</p>
<a name="boost_quaternions.quaternions.value_op.sup"></a><h5>
<a name="id528195"></a>
<a href="value_op.html#boost_quaternions.quaternions.value_op.sup">sup</a>
<a name="id784961"></a>
<a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.sup">sup</a>
</h5>
<p>
template&lt;typename T&gt; T sup(quaternion&lt;T&gt; const &amp; q);
@@ -60,8 +60,8 @@
This return the sup norm (the greatest among <code class="computeroutput"><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())...</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()))</span></code> of the quaternion.
</p>
<a name="boost_quaternions.quaternions.value_op.l1"></a><h5>
<a name="id528293"></a>
<a href="value_op.html#boost_quaternions.quaternions.value_op.l1">l1</a>
<a name="id785048"></a>
<a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.l1">l1</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">l1</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
</pre>
@@ -69,8 +69,8 @@
This return the l1 norm <code class="computeroutput"><span class="special">(</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_1</span><span class="special">())+...+</span><span class="identifier">abs</span><span class="special">(</span><span class="identifier">q</span><span class="special">.</span><span class="identifier">R_component_4</span><span class="special">()))</span></code> of the quaternion.
</p>
<a name="boost_quaternions.quaternions.value_op.abs"></a><h5>
<a name="id528486"></a>
<a href="value_op.html#boost_quaternions.quaternions.value_op.abs">abs</a>
<a name="id785217"></a>
<a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.abs">abs</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">abs</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
</pre>
@@ -78,8 +78,8 @@
This return the magnitude (Euclidian norm) of the quaternion.
</p>
<a name="boost_quaternions.quaternions.value_op.norm"></a><h5>
<a name="id528607"></a>
<a href="value_op.html#boost_quaternions.quaternions.value_op.norm">norm</a>
<a name="id785324"></a>
<a class="link" href="value_op.html#boost_quaternions.quaternions.value_op.norm">norm</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">&gt;</span> <span class="identifier">T</span> <span class="identifier">norm</span><span class="special">(</span><span class="identifier">quaternion</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;</span><span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">q</span><span class="special">);</span>
</pre>
@@ -93,7 +93,7 @@
</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 © 2001 -2003 Hubert Holin<p>
<td align="right"><div class="copyright-footer">Copyright &#169; 2001 -2003 Hubert Holin<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>
@@ -101,7 +101,7 @@
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@@ -17,8 +17,8 @@
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@@ -26,9 +26,9 @@
<div><div class="authorgroup"><div class="author"><h3 class="author">
<span class="firstname">Hubert</span> <span class="surname">Holin</span>
</h3></div></div></div>
<div><p class="copyright">Copyright © 2001 -2003 Hubert Holin</p></div>
<div><p class="copyright">Copyright &#169; 2001 -2003 Hubert Holin</p></div>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -76,6 +76,6 @@
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@@ -53,7 +53,7 @@
Hubert Holin, Xiaogang Zhang, Bruno Lalande, Johan R&#229;de, Gautam Sewani
and Thijs van den Berg</p></div>
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Distributed under the Boost Software License, Version 1.0. (See accompanying
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@@ -488,10 +488,10 @@
</p>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"><p><small>Last revised: April 13, 2010 at 12:21:17 GMT</small></p></td>
<td align="left"><p><small>Last revised: July 01, 2010 at 21:46:24 GMT</small></p></td>
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<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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@@ -20,9 +20,9 @@
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@@ -48,7 +48,7 @@
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@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
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@@ -20,9 +20,9 @@
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<a name="math_toolkit.backgrounders.implementation"></a><a class="link" href="implementation.html" title="Additional Implementation Notes"> Additional
Implementation Notes</a>
@@ -33,7 +33,7 @@
and reflect more the general implementation philosophy used.
</p>
<a name="math_toolkit.backgrounders.implementation.implemention_philosophy"></a><h5>
<a name="id1152410"></a>
<a name="id1092528"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.implemention_philosophy">Implemention
philosophy</a>
</h5>
@@ -85,7 +85,7 @@
These could still provide sufficient accuracy for some speed-critical applications.
</p>
<a name="math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values"></a><h5>
<a name="id1152474"></a>
<a name="id1092631"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.accuracy_and_representation_of_test_values">Accuracy
and Representation of Test Values</a>
</h5>
@@ -130,20 +130,20 @@
binary value).
</p>
<a name="math_toolkit.backgrounders.implementation.tolerance_of_tests"></a><h5>
<a name="id1152618"></a>
<a name="id1092820"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.tolerance_of_tests">Tolerance
of Tests</a>
</h5>
<p>
The tolerances need to be set to the maximum of:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
Some epsilon value.
</li>
<li>
The accuracy of the data (often only near 64-bit double).
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Some epsilon value.
</li>
<li class="listitem">
The accuracy of the data (often only near 64-bit double).
</li>
</ul></div>
<p>
Otherwise when long double has more digits than the test data, then no amount
@@ -156,7 +156,7 @@
first that the suffix L is present, and then that the tolerance is big enough.
</p>
<a name="math_toolkit.backgrounders.implementation.handling_unsuitable_arguments"></a><h5>
<a name="id1152655"></a>
<a name="id1092882"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_unsuitable_arguments">Handling
Unsuitable Arguments</a>
</h5>
@@ -166,49 +166,31 @@
it is proposed that signalling a domain error is mandatory when the argument
would give an mathematically undefined result.
</p>
<div class="itemizedlist"><ul type="disc"><li>
Guideline 1
</li></ul></div>
<div class="blockquote"><blockquote class="blockquote">
<p>
</p>
<p>
A mathematical function is said to be defined at a point a = (a1, a2,
. . .) if the limits as x = (x1, x2, . . .) 'approaches a from all directions
agree'. The defined value may be any number, or +infinity, or -infinity.
</p>
<p>
</p>
</blockquote></div>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
Guideline 1
</li></ul></div>
<div class="blockquote"><blockquote class="blockquote"><p>
A mathematical function is said to be defined at a point a = (a1, a2, .
. .) if the limits as x = (x1, x2, . . .) 'approaches a from all directions
agree'. The defined value may be any number, or +infinity, or -infinity.
</p></blockquote></div>
<p>
Put crudely, if the function goes to + infinity and then emerges 'round-the-back'
with - infinity, it is NOT defined.
</p>
<div class="blockquote"><blockquote class="blockquote">
<p>
</p>
<p>
The library function which approximates a mathematical function shall
signal a domain error whenever evaluated with argument values for which
the mathematical function is undefined.
</p>
<p>
</p>
</blockquote></div>
<div class="itemizedlist"><ul type="disc"><li>
Guideline 2
</li></ul></div>
<div class="blockquote"><blockquote class="blockquote">
<p>
</p>
<p>
The library function which approximates a mathematical function shall
signal a domain error whenever evaluated with argument values for which
the mathematical function obtains a non-real value.
</p>
<p>
</p>
</blockquote></div>
<div class="blockquote"><blockquote class="blockquote"><p>
The library function which approximates a mathematical function shall signal
a domain error whenever evaluated with argument values for which the mathematical
function is undefined.
</p></blockquote></div>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
Guideline 2
</li></ul></div>
<div class="blockquote"><blockquote class="blockquote"><p>
The library function which approximates a mathematical function shall signal
a domain error whenever evaluated with argument values for which the mathematical
function obtains a non-real value.
</p></blockquote></div>
<p>
This implementation is believed to follow these proposals and to assist compatibility
with <span class="emphasis"><em>ISO/IEC 9899:1999 Programming languages - C</em></span> and
@@ -229,7 +211,7 @@
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../doc/html/images/caution.png"></td>
<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>
@@ -242,7 +224,7 @@
</p></td></tr>
</table></div>
<a name="math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined"></a><h5>
<a name="id1152788"></a>
<a name="id1093073"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_functions_that_are_not_mathematically_defined">Handling
of Functions that are Not Mathematically defined</a>
</h5>
@@ -266,7 +248,7 @@
</p>
<div class="warning"><table border="0" summary="Warning">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../../../../doc/html/images/warning.png"></td>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../../../../../doc/src/images/warning.png"></td>
<th align="left">Warning</th>
</tr>
<tr><td align="left" valign="top"><p>
@@ -276,7 +258,7 @@
</p></td></tr>
</table></div>
<a name="math_toolkit.backgrounders.implementation.median_of_distributions"></a><h5>
<a name="id1152874"></a>
<a name="id1093197"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.median_of_distributions">Median
of distributions</a>
</h5>
@@ -309,7 +291,7 @@
Basic Statistics.</a> give more detail, in particular for discrete distributions.
</p>
<a name="math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity"></a><h5>
<a name="id1152971"></a>
<a name="id1093328"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.handling_of_floating_point_infinity">Handling
of Floating-Point Infinity</a>
</h5>
@@ -353,7 +335,7 @@
handling policies</a>.
</p>
<a name="math_toolkit.backgrounders.implementation.scale__shape_and_location"></a><h5>
<a name="id1153057"></a>
<a name="id1093470"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.scale__shape_and_location">Scale,
Shape and Location</a>
</h5>
@@ -380,19 +362,19 @@
functions, they can be added if required.
</p>
<a name="math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions"></a><h5>
<a name="id1153452"></a>
<a name="id1093880"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.notes_on_implementation_of_specific_functions__amp__distributions">Notes
on Implementation of Specific Functions &amp; Distributions</a>
</h5>
<div class="itemizedlist"><ul type="disc"><li>
Default parameters for the Triangular Distribution. We are uncertain about
the best default parameters. Some sources suggest that the Standard Triangular
Distribution has lower = 0, mode = half and upper = 1. However as a approximation
for the normal distribution, the most common usage, lower = -1, mode =
0 and upper = 1 would be more suitable.
</li></ul></div>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
Default parameters for the Triangular Distribution. We are uncertain
about the best default parameters. Some sources suggest that the Standard
Triangular Distribution has lower = 0, mode = half and upper = 1. However
as a approximation for the normal distribution, the most common usage,
lower = -1, mode = 0 and upper = 1 would be more suitable.
</li></ul></div>
<a name="math_toolkit.backgrounders.implementation.rational_approximations_used"></a><h5>
<a name="id1153472"></a>
<a name="id1093922"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.rational_approximations_used">Rational
Approximations Used</a>
</h5>
@@ -435,7 +417,7 @@
to the "true" minimax solution.
</p>
<a name="math_toolkit.backgrounders.implementation.representation_of_mathematical_constants"></a><h5>
<a name="id1153516"></a>
<a name="id1094010"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.representation_of_mathematical_constants">Representation
of Mathematical Constants</a>
</h5>
@@ -496,7 +478,7 @@
</span><span class="keyword">double</span> <span class="identifier">p</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">constants</span><span class="special">::</span><span class="identifier">pi</span><span class="special">();</span> <span class="comment">// Context does not allow for disambiguation of overloaded function
</span></pre>
<a name="math_toolkit.backgrounders.implementation.thread_safety"></a><h5>
<a name="id1153903"></a>
<a name="id1094488"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.thread_safety">Thread
safety</a>
</h5>
@@ -521,7 +503,7 @@
the right thing here at some point.
</p>
<a name="math_toolkit.backgrounders.implementation.sources_of_test_data"></a><h5>
<a name="id1153939"></a>
<a name="id1094549"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.sources_of_test_data">Sources
of Test Data</a>
</h5>
@@ -543,18 +525,12 @@
Is a Javascript application that calculates and plots probability distributions,
and provides the most complete range of distributions:
</p>
<div class="blockquote"><blockquote class="blockquote">
<p>
</p>
<p>
Bernoulli, Binomial, discrete uniform, geometric, hypergeometric, negative
binomial, Poisson, beta, Cauchy-Lorentz, chi-sequared, Erlang, exponential,
extreme value, Fisher, gamma, Laplace, logistic, lognormal, normal, Parteo,
Student's t, triangular, uniform, and Weibull.
</p>
<p>
</p>
</blockquote></div>
<div class="blockquote"><blockquote class="blockquote"><p>
Bernoulli, Binomial, discrete uniform, geometric, hypergeometric, negative
binomial, Poisson, beta, Cauchy-Lorentz, chi-sequared, Erlang, exponential,
extreme value, Fisher, gamma, Laplace, logistic, lognormal, normal, Parteo,
Student's t, triangular, uniform, and Weibull.
</p></blockquote></div>
<p>
It calculates pdf, cdf, survivor, log survivor, hazard, tail areas, &amp;
critical values for 5 tail values.
@@ -565,7 +541,7 @@
the underlying special function is known to be difficult to implement.
</p>
<a name="math_toolkit.backgrounders.implementation.creating_and_managing_the_equations"></a><h5>
<a name="id1154006"></a>
<a name="id1094648"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.creating_and_managing_the_equations">Creating
and Managing the Equations</a>
</h5>
@@ -737,7 +713,7 @@ done</pre>
HTML: this needs further investigation.
</p>
<a name="math_toolkit.backgrounders.implementation.producing_graphs"></a><h5>
<a name="id1154252"></a>
<a name="id1095018"></a>
<a class="link" href="implementation.html#math_toolkit.backgrounders.implementation.producing_graphs">Producing
Graphs</a>
</h5>
@@ -746,9 +722,9 @@ done</pre>
same process as the equations.
</p>
<p>
The programs /libs/math/doc/sf_and_dist/graphs/dist_graphs.cpp and /libs/math/doc/sf_and_dist/graphs<span class="emphasis"><em>sf_graphs.cpp
generate the SVG's directly using the [@http:</em></span>/code.google.com/soc/2007/boost/about.html
Google Summer of Code 2007] project of Jacob Voytko (whose work so far is
The programs /libs/math/doc/sf_and_dist/graphs/dist_graphs.cpp and /libs/math/doc/sf_and_dist/graphs/sf_graphs.cpp
generate the SVG's directly using the <a href="http://code.google.com/soc/2007/boost/about.html" target="_top">Google
Summer of Code 2007</a> project of Jacob Voytko (whose work so far is
at .\boost-sandbox\SOC\2007\visualization).
</p>
</div>
@@ -764,7 +740,7 @@ done</pre>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../backgrounders.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="relative_error.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="../backgrounders.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.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="relative_error.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>The Lanczos Approximation</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../backgrounders.html" title="Backgrounders">
<link rel="prev" href="relative_error.html" title="Relative Error">
@@ -20,14 +20,14 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="relative_error.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="remez.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="relative_error.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.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="remez.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.backgrounders.lanczos"></a><a class="link" href="lanczos.html" title="The Lanczos Approximation"> The Lanczos Approximation</a>
</h3></div></div></div>
<a name="math_toolkit.backgrounders.lanczos.motivation"></a><h5>
<a name="id1154475"></a>
<a name="id1095332"></a>
<a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.motivation">Motivation</a>
</h5>
<p>
@@ -45,19 +45,20 @@
Lanczos approximation does have a couple of properties that make it worthy
of further consideration:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
The approximation has an easy to compute truncation error that holds for
all <span class="emphasis"><em>z &gt; 0</em></span>. In practice that means we can use the
same approximation for all <span class="emphasis"><em>z &gt; 0</em></span>, and be certain
that no matter how large or small <span class="emphasis"><em>z</em></span> is, the truncation
error will <span class="emphasis"><em>at worst</em></span> be bounded by some finite value.
</li>
<li>
The approximation has a form that is particularly amenable to analytic
manipulation, in particular ratios of gamma or gamma-like functions are
particularly easy to compute without resorting to logarithms.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
The approximation has an easy to compute truncation error that holds
for all <span class="emphasis"><em>z &gt; 0</em></span>. In practice that means we can
use the same approximation for all <span class="emphasis"><em>z &gt; 0</em></span>, and
be certain that no matter how large or small <span class="emphasis"><em>z</em></span> is,
the truncation error will <span class="emphasis"><em>at worst</em></span> be bounded by
some finite value.
</li>
<li class="listitem">
The approximation has a form that is particularly amenable to analytic
manipulation, in particular ratios of gamma or gamma-like functions are
particularly easy to compute without resorting to logarithms.
</li>
</ul></div>
<p>
It is the combination of these two properties that make the approximation
@@ -98,7 +99,7 @@
functions divided by large powers into single (simpler) expressions.
</p>
<a name="math_toolkit.backgrounders.lanczos.the_approximation"></a><h5>
<a name="id1154725"></a>
<a name="id1095672"></a>
<a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.the_approximation">The
Approximation</a>
</h5>
@@ -148,7 +149,7 @@
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/html/images/note.png"></td>
<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>
@@ -160,7 +161,7 @@
</p></td></tr>
</table></div>
<a name="math_toolkit.backgrounders.lanczos.computing_the_coefficients"></a><h5>
<a name="id1154917"></a>
<a name="id1095908"></a>
<a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.computing_the_coefficients">Computing
the Coefficients</a>
</h5>
@@ -204,7 +205,7 @@
multiplied by <span class="emphasis"><em>F</em></span> as the last step.
</p>
<a name="math_toolkit.backgrounders.lanczos.choosing_the_right_parameters"></a><h5>
<a name="id1155074"></a>
<a name="id1096092"></a>
<a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.choosing_the_right_parameters">Choosing
the Right Parameters</a>
</h5>
@@ -228,10 +229,10 @@
computing to float precision with double precision arithmetic.
</p>
<div class="table">
<a name="id1155128"></a><p class="title"><b>Table&#160;53.&#160;Optimal choices for N and g when computing with
guard digits (source: Pugh)</b></p>
<div class="table-contents"><table class="table" summary="Optimal choices for N and g when computing with
guard digits (source: Pugh)">
<a name="id1096168"></a><p class="title"><b>Table&#160;53.&#160;Optimal choices for N and g when computing with guard digits (source:
Pugh)</b></p>
<div class="table-contents"><table class="table" summary="Optimal choices for N and g when computing with guard digits (source:
Pugh)">
<colgroup>
<col>
<col>
@@ -240,70 +241,70 @@
</colgroup>
<thead><tr>
<th>
<p>
Significand Size
</p>
</th>
<p>
Significand Size
</p>
</th>
<th>
<p>
N
</p>
</th>
<p>
N
</p>
</th>
<th>
<p>
g
</p>
</th>
<p>
g
</p>
</th>
<th>
<p>
Max Error
</p>
</th>
<p>
Max Error
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
24
</p>
</td>
<p>
24
</p>
</td>
<td>
<p>
6
</p>
</td>
<p>
6
</p>
</td>
<td>
<p>
5.581
</p>
</td>
<p>
5.581
</p>
</td>
<td>
<p>
9.51e-12
</p>
</td>
<p>
9.51e-12
</p>
</td>
</tr>
<tr>
<td>
<p>
53
</p>
</td>
<p>
53
</p>
</td>
<td>
<p>
13
</p>
</td>
<p>
13
</p>
</td>
<td>
<p>
13.144565
</p>
</td>
<p>
13.144565
</p>
</td>
<td>
<p>
9.2213e-23
</p>
</td>
<p>
9.2213e-23
</p>
</td>
</tr>
</tbody>
</table></div>
@@ -371,10 +372,8 @@
exactly matches the machine epsilon for the type in question.
</p>
<div class="table">
<a name="id1155339"></a><p class="title"><b>Table&#160;54.&#160;Optimum value for N and g when computing at fixed
precision</b></p>
<div class="table-contents"><table class="table" summary="Optimum value for N and g when computing at fixed
precision">
<a name="id1096444"></a><p class="title"><b>Table&#160;54.&#160;Optimum value for N and g when computing at fixed precision</b></p>
<div class="table-contents"><table class="table" summary="Optimum value for N and g when computing at fixed precision">
<colgroup>
<col>
<col>
@@ -384,139 +383,139 @@
</colgroup>
<thead><tr>
<th>
<p>
Significand Size
</p>
</th>
<p>
Significand Size
</p>
</th>
<th>
<p>
Platform/Compiler Used
</p>
</th>
<p>
Platform/Compiler Used
</p>
</th>
<th>
<p>
N
</p>
</th>
<p>
N
</p>
</th>
<th>
<p>
g
</p>
</th>
<p>
g
</p>
</th>
<th>
<p>
Max Truncation Error
</p>
</th>
<p>
Max Truncation Error
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
24
</p>
</td>
<p>
24
</p>
</td>
<td>
<p>
Win32, VC++ 7.1
</p>
</td>
<p>
Win32, VC++ 7.1
</p>
</td>
<td>
<p>
6
</p>
</td>
<p>
6
</p>
</td>
<td>
<p>
1.428456135094165802001953125
</p>
</td>
<p>
1.428456135094165802001953125
</p>
</td>
<td>
<p>
9.41e-007
</p>
</td>
<p>
9.41e-007
</p>
</td>
</tr>
<tr>
<td>
<p>
53
</p>
</td>
<p>
53
</p>
</td>
<td>
<p>
Win32, VC++ 7.1
</p>
</td>
<p>
Win32, VC++ 7.1
</p>
</td>
<td>
<p>
13
</p>
</td>
<p>
13
</p>
</td>
<td>
<p>
6.024680040776729583740234375
</p>
</td>
<p>
6.024680040776729583740234375
</p>
</td>
<td>
<p>
3.23e-016
</p>
</td>
<p>
3.23e-016
</p>
</td>
</tr>
<tr>
<td>
<p>
64
</p>
</td>
<p>
64
</p>
</td>
<td>
<p>
Suse Linux 9 IA64, gcc-3.3.3
</p>
</td>
<p>
Suse Linux 9 IA64, gcc-3.3.3
</p>
</td>
<td>
<p>
17
</p>
</td>
<p>
17
</p>
</td>
<td>
<p>
12.2252227365970611572265625
</p>
</td>
<p>
12.2252227365970611572265625
</p>
</td>
<td>
<p>
2.34e-024
</p>
</td>
<p>
2.34e-024
</p>
</td>
</tr>
<tr>
<td>
<p>
116
</p>
</td>
<p>
116
</p>
</td>
<td>
<p>
HP Tru64 Unix 5.1B / Alpha, Compaq C++ V7.1-006
</p>
</td>
<p>
HP Tru64 Unix 5.1B / Alpha, Compaq C++ V7.1-006
</p>
</td>
<td>
<p>
24
</p>
</td>
<p>
24
</p>
</td>
<td>
<p>
20.3209821879863739013671875
</p>
</td>
<p>
20.3209821879863739013671875
</p>
</td>
<td>
<p>
4.75e-035
</p>
</td>
<p>
4.75e-035
</p>
</td>
</tr>
</tbody>
</table></div>
@@ -536,27 +535,27 @@
is exact, and so isn't used for the gamma function.
</p>
<a name="math_toolkit.backgrounders.lanczos.references"></a><h5>
<a name="id1156975"></a>
<a name="id1096414"></a>
<a class="link" href="lanczos.html#math_toolkit.backgrounders.lanczos.references">References</a>
</h5>
<a name="godfrey"></a><a name="pugh"></a><div class="orderedlist"><ol type="1">
<li>
Paul Godfrey, <a href="http://my.fit.edu/~gabdo/gamma.txt" target="_top">"A note
on the computation of the convergent Lanczos complex Gamma approximation"</a>.
</li>
<li>
Glendon Ralph Pugh, <a href="http://bh0.physics.ubc.ca/People/matt/Doc/ThesesOthers/Phd/pugh.pdf" target="_top">"An
Analysis of the Lanczos Gamma Approximation"</a>, PhD Thesis November
2004.
</li>
<li>
Viktor T. Toth, <a href="http://www.rskey.org/gamma.htm" target="_top">"Calculators
and the Gamma Function"</a>.
</li>
<li>
Mathworld, <a href="http://mathworld.wolfram.com/LanczosApproximation.html" target="_top">The
Lanczos Approximation</a>.
</li>
<a name="godfrey"></a><a name="pugh"></a><div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
Paul Godfrey, <a href="http://my.fit.edu/~gabdo/gamma.txt" target="_top">"A
note on the computation of the convergent Lanczos complex Gamma approximation"</a>.
</li>
<li class="listitem">
Glendon Ralph Pugh, <a href="http://bh0.physics.ubc.ca/People/matt/Doc/ThesesOthers/Phd/pugh.pdf" target="_top">"An
Analysis of the Lanczos Gamma Approximation"</a>, PhD Thesis
November 2004.
</li>
<li class="listitem">
Viktor T. Toth, <a href="http://www.rskey.org/gamma.htm" target="_top">"Calculators
and the Gamma Function"</a>.
</li>
<li class="listitem">
Mathworld, <a href="http://mathworld.wolfram.com/LanczosApproximation.html" target="_top">The
Lanczos Approximation</a>.
</li>
</ol></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -571,7 +570,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="relative_error.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="remez.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="relative_error.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.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="remez.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
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@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>References</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../backgrounders.html" title="Backgrounders">
<link rel="prev" href="remez.html" title="The Remez Method">
@@ -20,14 +20,14 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="remez.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../status.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="remez.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.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="../status.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.backgrounders.refs"></a><a class="link" href="refs.html" title="References"> References</a>
</h3></div></div></div>
<a name="math_toolkit.backgrounders.refs.general_references"></a><h5>
<a name="id1157845"></a>
<a name="id1097925"></a>
<a class="link" href="refs.html#math_toolkit.backgrounders.refs.general_references">General
references</a>
</h5>
@@ -91,7 +91,7 @@
Library (version 2), Walter E. Brown</a>
</p>
<a name="math_toolkit.backgrounders.refs.calculators__that_we_found__and_used_to_cross_check___as_far_as_their_widely_varying_accuracy_allowed__"></a><h5>
<a name="id1157941"></a>
<a name="id1098035"></a>
<a class="link" href="refs.html#math_toolkit.backgrounders.refs.calculators__that_we_found__and_used_to_cross_check___as_far_as_their_widely_varying_accuracy_allowed__">Calculators*
that we found (and used to cross-check - as far as their widely-varying accuracy
allowed).</a>
@@ -101,7 +101,7 @@
Binomial Probability Distribution Calculator.
</p>
<a name="math_toolkit.backgrounders.refs.other_libraries"></a><h5>
<a name="id1157966"></a>
<a name="id1098077"></a>
<a class="link" href="refs.html#math_toolkit.backgrounders.refs.other_libraries">Other Libraries</a>
</h5>
<p>
@@ -171,7 +171,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="remez.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../status.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="remez.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.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="../status.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
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@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Relative Error</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../backgrounders.html" title="Backgrounders">
<link rel="prev" href="implementation.html" title="Additional Implementation Notes">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="implementation.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lanczos.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="implementation.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.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="lanczos.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.backgrounders.relative_error"></a><a class="link" href="relative_error.html" title="Relative Error"> Relative
Error</a>
@@ -81,7 +81,7 @@
<a name="zero_error"></a><p>
</p>
<a name="math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error"></a><h5>
<a name="id1154432"></a>
<a name="id1095263"></a>
<a class="link" href="relative_error.html#math_toolkit.backgrounders.relative_error.the_impossibility_of_zero_error">The
Impossibility of Zero Error</a>
</h5>
@@ -119,7 +119,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="implementation.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lanczos.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="implementation.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.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="lanczos.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
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@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>The Remez Method</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../backgrounders.html" title="Backgrounders">
<link rel="prev" href="lanczos.html" title="The Lanczos Approximation">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="lanczos.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="refs.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="lanczos.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.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="refs.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.backgrounders.remez"></a><a class="link" href="remez.html" title="The Remez Method"> The Remez Method</a>
</h3></div></div></div>
@@ -65,17 +65,17 @@
yields the smallest maximal value of the error function. Chebyshev showed
that there is a unique minimax solution for R(x) that has the following properties:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
If R(x) is a polynomial of degree N, then there are N+2 unknowns: the N+1
coefficients of the polynomial, and maximal value of the error function.
</li>
<li>
The error function has N+1 roots, and N+2 extrema (minima and maxima).
</li>
<li>
The extrema alternate in sign, and all have the same magnitude.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
If R(x) is a polynomial of degree N, then there are N+2 unknowns: the
N+1 coefficients of the polynomial, and maximal value of the error function.
</li>
<li class="listitem">
The error function has N+1 roots, and N+2 extrema (minima and maxima).
</li>
<li class="listitem">
The extrema alternate in sign, and all have the same magnitude.
</li>
</ul></div>
<p>
That means that if we know the location of the extrema of the error function
@@ -94,7 +94,7 @@
are located!</em></span>
</p>
<a name="math_toolkit.backgrounders.remez.the_remez_method"></a><h5>
<a name="id1157135"></a>
<a name="id1096963"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.the_remez_method">The Remez
Method</a>
</h5>
@@ -150,7 +150,7 @@
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../doc/html/images/note.png"></td>
<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">
@@ -174,7 +174,7 @@
</td></tr>
</table></div>
<a name="math_toolkit.backgrounders.remez.remez_step_1"></a><h5>
<a name="id1157286"></a>
<a name="id1097153"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_step_1">Remez Step
1</a>
</h5>
@@ -205,7 +205,7 @@
to 5.6x10<sup>-4</sup>.
</p>
<a name="math_toolkit.backgrounders.remez.remez_step_2"></a><h5>
<a name="id1157360"></a>
<a name="id1097248"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_step_2">Remez Step
2</a>
</h5>
@@ -234,7 +234,7 @@
In our example we perform multi-point exchange.
</p>
<a name="math_toolkit.backgrounders.remez.iteration"></a><h5>
<a name="id1157393"></a>
<a name="id1097293"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.iteration">Iteration</a>
</h5>
<p>
@@ -250,7 +250,7 @@
<span class="inlinemediaobject"><img src="../../../graphs/remez-4.png" alt="remez-4"></span>
</p>
<a name="math_toolkit.backgrounders.remez.rational_approximations"></a><h5>
<a name="id1157437"></a>
<a name="id1097348"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.rational_approximations">Rational
Approximations</a>
</h5>
@@ -299,7 +299,7 @@
number of terms overall.
</p>
<a name="math_toolkit.backgrounders.remez.practical_considerations"></a><h5>
<a name="id1157516"></a>
<a name="id1097450"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.practical_considerations">Practical
Considerations</a>
</h5>
@@ -407,7 +407,7 @@
desired minimax solution (5x10<sup>-4</sup>).
</p>
<a name="math_toolkit.backgrounders.remez.remez_method_checklist"></a><h5>
<a name="id1157672"></a>
<a name="id1097648"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.remez_method_checklist">Remez
Method Checklist</a>
</h5>
@@ -416,52 +416,52 @@
wrong, it is by no means an exhaustive list, but is provided in the hopes
that it will prove useful.
</p>
<div class="itemizedlist"><ul type="disc">
<li>
Is the function smooth enough? Can it be better separated into a rapidly
changing part, and an asymptotic part?
</li>
<li>
Does the function being approximated have any "blips" in it?
Check for problems as the function changes computation method, or if a
root, or an infinity has been divided out. The telltale sign is if there
is a narrow region where the Remez method will not converge.
</li>
<li>
Check you have enough accuracy in your calculations: remember that the
Remez method works on the difference between the approximation and the
function being approximated: so you must have more digits of precision
available than the precision of the approximation being constructed. So
for example at double precision, you shouldn't expect to be able to get
better than a float precision approximation.
</li>
<li>
Try skewing the initial interpolated approximation to minimise the error
before you begin the Remez steps.
</li>
<li>
If the approximation won't converge or is ill-conditioned from one starting
location, try starting from a different location.
</li>
<li>
If a rational function won't converge, one can minimise a polynomial (which
presents no problems), then rotate one term from the numerator to the denominator
and minimise again. In theory one can continue moving terms one at a time
from numerator to denominator, and then re-minimising, retaining the last
set of control points at each stage.
</li>
<li>
Try using a smaller interval. It may also be possible to optimise over
one (small) interval, rescale the control points over a larger interval,
and then re-minimise.
</li>
<li>
Keep absissa values small: use a change of variable to keep the abscissa
over, say [0, b], for some smallish value <span class="emphasis"><em>b</em></span>.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
Is the function smooth enough? Can it be better separated into a rapidly
changing part, and an asymptotic part?
</li>
<li class="listitem">
Does the function being approximated have any "blips" in it?
Check for problems as the function changes computation method, or if
a root, or an infinity has been divided out. The telltale sign is if
there is a narrow region where the Remez method will not converge.
</li>
<li class="listitem">
Check you have enough accuracy in your calculations: remember that the
Remez method works on the difference between the approximation and the
function being approximated: so you must have more digits of precision
available than the precision of the approximation being constructed.
So for example at double precision, you shouldn't expect to be able to
get better than a float precision approximation.
</li>
<li class="listitem">
Try skewing the initial interpolated approximation to minimise the error
before you begin the Remez steps.
</li>
<li class="listitem">
If the approximation won't converge or is ill-conditioned from one starting
location, try starting from a different location.
</li>
<li class="listitem">
If a rational function won't converge, one can minimise a polynomial
(which presents no problems), then rotate one term from the numerator
to the denominator and minimise again. In theory one can continue moving
terms one at a time from numerator to denominator, and then re-minimising,
retaining the last set of control points at each stage.
</li>
<li class="listitem">
Try using a smaller interval. It may also be possible to optimise over
one (small) interval, rescale the control points over a larger interval,
and then re-minimise.
</li>
<li class="listitem">
Keep absissa values small: use a change of variable to keep the abscissa
over, say [0, b], for some smallish value <span class="emphasis"><em>b</em></span>.
</li>
</ul></div>
<a name="math_toolkit.backgrounders.remez.references"></a><h5>
<a name="id1157725"></a>
<a name="id1097762"></a>
<a class="link" href="remez.html#math_toolkit.backgrounders.remez.references">References</a>
</h5>
<p>
@@ -537,7 +537,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="lanczos.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../backgrounders.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="refs.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
</body>
</html>

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@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Statistical Distributions and Functions</title>
<link rel="stylesheet" href="../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../index.html" title="Math Toolkit">
<link rel="up" href="../index.html" title="Math Toolkit">
<link rel="prev" href="main_overview/contact.html" title="Contact Info and Support">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="main_overview/contact.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dist/stat_tut.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="main_overview/contact.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="dist/stat_tut.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="math_toolkit.dist"></a><a class="link" href="dist.html" title="Statistical Distributions and Functions"> Statistical Distributions and Functions</a>
</h2></div></div></div>
@@ -208,7 +208,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="main_overview/contact.html"><img src="../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.html"><img src="../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../index.html"><img src="../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dist/stat_tut.html"><img src="../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="main_overview/contact.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../index.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="dist/stat_tut.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Statistical Distributions Reference</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../dist.html" title="Statistical Distributions and Functions">
<link rel="prev" href="stat_tut/dist_params.html" title="Discrete Probability Distributions">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="stat_tut/dist_params.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dist_ref/nmp.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="stat_tut/dist_params.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.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="dist_ref/nmp.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.dist.dist_ref"></a><a class="link" href="dist_ref.html" title="Statistical Distributions Reference"> Statistical Distributions
Reference</a>
@@ -99,7 +99,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="stat_tut/dist_params.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dist_ref/nmp.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="stat_tut/dist_params.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.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="dist_ref/nmp.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Distribution Algorithms</title>
<link rel="stylesheet" href="../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dist_ref.html" title="Statistical Distributions Reference">
<link rel="prev" href="dists/uniform_dist.html" title="Uniform Distribution">
@@ -20,15 +20,15 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="dists/uniform_dist.html"><img src="../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../future.html"><img src="../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="dists/uniform_dist.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.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="../future.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist.dist_ref.dist_algorithms"></a><a class="link" href="dist_algorithms.html" title="Distribution Algorithms"> Distribution
Algorithms</a>
</h4></div></div></div>
<a name="math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions"></a><h5>
<a name="id936653"></a>
<a name="id900389"></a>
<a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.finding_the_location_and_scale_for_normal_and_similar_distributions">Finding
the Location and Scale for Normal and similar distributions</a>
</h5>
@@ -50,7 +50,7 @@
</span><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">complement</span><span class="special">;</span> <span class="comment">// Will be needed by users who want to use complements.
</span></pre>
<a name="math_toolkit.dist.dist_ref.dist_algorithms.find_location_function"></a><h5>
<a name="id936752"></a>
<a name="id900525"></a>
<a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_location_function">find_location
function</a>
</h5>
@@ -80,7 +80,7 @@
<span class="special">}}</span> <span class="comment">// namespaces
</span></pre>
<a name="math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function"></a><h5>
<a name="id937197"></a>
<a name="id901071"></a>
<a class="link" href="dist_algorithms.html#math_toolkit.dist.dist_ref.dist_algorithms.find_scale_function">find_scale
function</a>
</h5>
@@ -140,7 +140,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="dists/uniform_dist.html"><img src="../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../future.html"><img src="../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="dists/uniform_dist.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.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="../future.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Distributions</title>
<link rel="stylesheet" href="../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dist_ref.html" title="Statistical Distributions Reference">
<link rel="prev" href="nmp.html" title="Non-Member Properties">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="nmp.html"><img src="../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dists/bernoulli_dist.html"><img src="../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="nmp.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.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="dists/bernoulli_dist.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist.dist_ref.dists"></a><a class="link" href="dists.html" title="Distributions"> Distributions</a>
</h4></div></div></div>
@@ -92,7 +92,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="nmp.html"><img src="../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dists/bernoulli_dist.html"><img src="../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="nmp.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.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="dists/bernoulli_dist.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Bernoulli Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="../dists.html" title="Distributions">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../dists.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="beta_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="../dists.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="beta_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist"></a><a class="link" href="bernoulli_dist.html" title="Bernoulli Distribution">
Bernoulli Distribution</a>
@@ -87,7 +87,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/bernoulli_cdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions"></a><h5>
<a name="id881938"></a>
<a name="id852613"></a>
<a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.member_functions">Member
Functions</a>
</h5>
@@ -103,7 +103,7 @@
Returns the <span class="emphasis"><em>success_fraction</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors"></a><h5>
<a name="id882016"></a>
<a name="id852717"></a>
<a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -128,7 +128,7 @@
exception and make an error message available.
</p>
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy"></a><h5>
<a name="id882119"></a>
<a name="id852870"></a>
<a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -136,7 +136,7 @@
and so should have errors within an epsilon or two.
</p>
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation"></a><h5>
<a name="id882141"></a>
<a name="id852898"></a>
<a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.implementation">Implementation</a>
</h5>
<p>
@@ -146,7 +146,7 @@
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../../doc/html/images/note.png"></td>
<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">
@@ -169,172 +169,176 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
Supported range
</p>
<p>
Supported range
</p>
</td>
<td>
<p>
{0, 1}
</p>
<p>
{0, 1}
</p>
</td>
</tr>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = 1 - p for k = 0, else p
</p>
<p>
Using the relation: pdf = 1 - p for k = 0, else p
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: cdf = 1 - p for k = 0, else 1
</p>
<p>
Using the relation: cdf = 1 - p for k = 0, else 1
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
q = 1 - p
</p>
<p>
q = 1 - p
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
if x &lt;= (1-p) 0 else 1
</p>
<p>
if x &lt;= (1-p) 0 else 1
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
if x &lt;= (1-p) 1 else 0
</p>
<p>
if x &lt;= (1-p) 1 else 0
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
p
</p>
<p>
p
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
p * (1 - p)
</p>
<p>
p * (1 - p)
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
if (p &lt; 0.5) 0 else 1
</p>
<p>
if (p &lt; 0.5) 0 else 1
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
(1 - 2 * p) / sqrt(p * q)
</p>
<p>
(1 - 2 * p) / sqrt(p * q)
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
6 * p * p - 6 * p +1/ p * q
</p>
<p>
6 * p * p - 6 * p +1/ p * q
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
kurtosis -3
</p>
<p>
kurtosis -3
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.bernoulli_dist.references"></a><h5>
<a name="id882452"></a>
<a name="id853248"></a>
<a class="link" href="bernoulli_dist.html#math_toolkit.dist.dist_ref.dists.bernoulli_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li><a href="http://en.wikipedia.org/wiki/Bernoulli_distribution" target="_top">Wikpedia
Bernoulli distribution</a></li>
<li><a href="../../../../" target="_top">Weisstein, Eric W. "Bernoulli Distribution."
From MathWorld--A Wolfram Web Resource.</a></li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a href="http://en.wikipedia.org/wiki/Bernoulli_distribution" target="_top">Wikpedia
Bernoulli distribution</a>
</li>
<li class="listitem">
<a href="../../../../" target="_top">Weisstein, Eric W. "Bernoulli Distribution."
From MathWorld--A Wolfram Web Resource.</a>
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -349,7 +353,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../dists.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="beta_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="../dists.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="beta_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Beta Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="bernoulli_dist.html" title="Bernoulli Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="bernoulli_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="binomial_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="bernoulli_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="binomial_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.beta_dist"></a><a class="link" href="beta_dist.html" title="Beta Distribution"> Beta
Distribution</a>
@@ -133,12 +133,12 @@
from the centre (where x = half).
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.member_functions"></a><h5>
<a name="id883259"></a>
<a name="id854240"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.member_functions">Member
Functions</a>
</h5>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.constructor"></a><h6>
<a name="id883275"></a>
<a name="id854269"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.constructor">Constructor</a>
</h6>
<pre class="programlisting"><span class="identifier">beta_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">beta</span><span class="special">);</span>
@@ -165,7 +165,7 @@
yellow in the graph above).
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors"></a><h6>
<a name="id883390"></a>
<a name="id854414"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.parameter_accessors">Parameter
Accessors</a>
</h6>
@@ -189,7 +189,7 @@
</span><span class="identifier">assert</span><span class="special">(</span><span class="identifier">mybeta</span><span class="special">.</span><span class="identifier">beta</span><span class="special">()</span> <span class="special">==</span> <span class="number">5.</span><span class="special">);</span> <span class="comment">// mybeta.beta() returns 5
</span></pre>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators"></a><h5>
<a name="id883592"></a>
<a name="id854658"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.parameter_estimators">Parameter
Estimators</a>
</h5>
@@ -242,7 +242,7 @@ from presumed-known mean and variance.
Returns the value of &#946; that gives: <code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">beta_distribution</span><span class="special">&lt;</span><span class="identifier">RealType</span><span class="special">&gt;(</span><span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">beta</span><span class="special">),</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">probability</span></code>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.non_member_accessor_functions"></a><h5>
<a name="id885786"></a>
<a name="id855217"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.non_member_accessor_functions">Non-member
Accessor Functions</a>
</h5>
@@ -264,7 +264,7 @@ from presumed-known mean and variance.
Mathworld</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.applications"></a><h5>
<a name="id885888"></a>
<a name="id855371"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.applications">Applications</a>
</h5>
<p>
@@ -277,7 +277,7 @@ from presumed-known mean and variance.
statistical inference</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions"></a><h5>
<a name="id885914"></a>
<a name="id855412"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.related_distributions">Related
distributions</a>
</h5>
@@ -303,7 +303,7 @@ from presumed-known mean and variance.
Distribution</a> with its p parameter set to x.
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.accuracy"></a><h5>
<a name="id885960"></a>
<a name="id855483"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -315,7 +315,7 @@ from presumed-known mean and variance.
please refer to these functions for information on accuracy.
</p>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.implementation"></a><h5>
<a name="id886005"></a>
<a name="id855554"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.implementation">Implementation</a>
</h5>
<p>
@@ -330,274 +330,273 @@ from presumed-known mean and variance.
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
f(x;&#945;,&#946;) = x<sup>&#945; - 1</sup> (1 - x)<sup>&#946; -1</sup> / B(&#945;, &#946;)
</p>
<p>
Implemented using <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>(a,
b, x).
</p>
<p>
f(x;&#945;,&#946;) = x<sup>&#945; - 1</sup> (1 - x)<sup>&#946; -1</sup> / B(&#945;, &#946;)
</p>
<p>
Implemented using <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>(a,
b, x).
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the incomplete beta function <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(a,
b, x)
</p>
<p>
Using the incomplete beta function <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(a,
b, x)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
<a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>(a,
b, x)
</p>
<p>
<a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>(a,
b, x)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the inverse incomplete beta function <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>(a,
b, p)
</p>
<p>
Using the inverse incomplete beta function <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>(a,
b, p)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
<a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>(a,
b, q)
</p>
<p>
<a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>(a,
b, q)
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">a</span><span class="special">/(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">)</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">a</span><span class="special">/(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">a</span> <span class="special">*</span>
<span class="identifier">b</span> <span class="special">/</span>
<span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">)^</span><span class="number">2</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">a</span> <span class="special">+</span>
<span class="identifier">b</span> <span class="special">+</span>
<span class="number">1</span><span class="special">)</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">a</span> <span class="special">*</span>
<span class="identifier">b</span> <span class="special">/</span>
<span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">)^</span><span class="number">2</span>
<span class="special">*</span> <span class="special">(</span><span class="identifier">a</span> <span class="special">+</span>
<span class="identifier">b</span> <span class="special">+</span>
<span class="number">1</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">(</span><span class="identifier">a</span><span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">/</span>
<span class="special">(</span><span class="identifier">a</span>
<span class="special">+</span> <span class="identifier">b</span>
<span class="special">-</span> <span class="number">2</span><span class="special">)</span></code>
</p>
<p>
<code class="computeroutput"><span class="special">(</span><span class="identifier">a</span><span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">/</span>
<span class="special">(</span><span class="identifier">a</span>
<span class="special">+</span> <span class="identifier">b</span>
<span class="special">-</span> <span class="number">2</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">2</span> <span class="special">(</span><span class="identifier">b</span><span class="special">-</span><span class="identifier">a</span><span class="special">)</span>
<span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">+</span><span class="number">1</span><span class="special">)/(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">+</span><span class="number">2</span><span class="special">)</span> <span class="special">*</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span>
<span class="special">*</span> <span class="identifier">b</span><span class="special">)</span></code>
</p>
<p>
<code class="computeroutput"><span class="number">2</span> <span class="special">(</span><span class="identifier">b</span><span class="special">-</span><span class="identifier">a</span><span class="special">)</span>
<span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">+</span><span class="number">1</span><span class="special">)/(</span><span class="identifier">a</span><span class="special">+</span><span class="identifier">b</span><span class="special">+</span><span class="number">2</span><span class="special">)</span>
<span class="special">*</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">a</span>
<span class="special">*</span> <span class="identifier">b</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/beta_dist_kurtosis.png"></span>
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/beta_dist_kurtosis.png"></span>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">kurtosis</span> <span class="special">+</span>
<span class="number">3</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">kurtosis</span> <span class="special">+</span>
<span class="number">3</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
parameter estimation
</p>
<p>
parameter estimation
</p>
</td>
<td>
<p>
</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
alpha
</p>
<p>
from mean and variance
</p>
<p>
alpha
</p>
<p>
from mean and variance
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">mean</span> <span class="special">*</span>
<span class="special">((</span> <span class="special">(</span><span class="identifier">mean</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">mean</span><span class="special">))</span> <span class="special">/</span>
<span class="identifier">variance</span><span class="special">)-</span>
<span class="number">1</span><span class="special">)</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">mean</span> <span class="special">*</span>
<span class="special">((</span> <span class="special">(</span><span class="identifier">mean</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">mean</span><span class="special">))</span> <span class="special">/</span>
<span class="identifier">variance</span><span class="special">)-</span>
<span class="number">1</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
beta
</p>
<p>
from mean and variance
</p>
<p>
beta
</p>
<p>
from mean and variance
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">mean</span><span class="special">)</span> <span class="special">*</span>
<span class="special">(((</span><span class="identifier">mean</span>
<span class="special">*</span> <span class="special">(</span><span class="number">1</span> <span class="special">-</span> <span class="identifier">mean</span><span class="special">))</span>
<span class="special">/</span><span class="identifier">variance</span><span class="special">)-</span><span class="number">1</span><span class="special">)</span></code>
</p>
<p>
<code class="computeroutput"><span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">mean</span><span class="special">)</span> <span class="special">*</span>
<span class="special">(((</span><span class="identifier">mean</span>
<span class="special">*</span> <span class="special">(</span><span class="number">1</span> <span class="special">-</span>
<span class="identifier">mean</span><span class="special">))</span>
<span class="special">/</span><span class="identifier">variance</span><span class="special">)-</span><span class="number">1</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
The member functions <code class="computeroutput"><span class="identifier">find_alpha</span></code>
and <code class="computeroutput"><span class="identifier">find_beta</span></code>
</p>
<p>
from cdf and probability x
</p>
<p>
and <span class="bold"><strong>either</strong></span> <code class="computeroutput"><span class="identifier">alpha</span></code>
or <code class="computeroutput"><span class="identifier">beta</span></code>
</p>
<p>
The member functions <code class="computeroutput"><span class="identifier">find_alpha</span></code>
and <code class="computeroutput"><span class="identifier">find_beta</span></code>
</p>
<p>
from cdf and probability x
</p>
<p>
and <span class="bold"><strong>either</strong></span> <code class="computeroutput"><span class="identifier">alpha</span></code>
or <code class="computeroutput"><span class="identifier">beta</span></code>
</p>
</td>
<td>
<p>
Implemented in terms of the inverse incomplete beta functions
</p>
<p>
<a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a>,
and <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a>
respectively.
</p>
<p>
Implemented in terms of the inverse incomplete beta functions
</p>
<p>
<a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inva</a>,
and <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_invb</a>
respectively.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">find_alpha</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">find_alpha</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">ibeta_inva</span><span class="special">(</span><span class="identifier">beta</span><span class="special">,</span>
<span class="identifier">x</span><span class="special">,</span>
<span class="identifier">probability</span><span class="special">)</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">ibeta_inva</span><span class="special">(</span><span class="identifier">beta</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">probability</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">find_beta</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">find_beta</span></code>
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">ibeta_invb</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">,</span>
<span class="identifier">x</span><span class="special">,</span>
<span class="identifier">probability</span><span class="special">)</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">ibeta_invb</span><span class="special">(</span><span class="identifier">alpha</span><span class="special">,</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">probability</span><span class="special">)</span></code>
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.beta_dist.references"></a><h5>
<a name="id887013"></a>
<a name="id856997"></a>
<a class="link" href="beta_dist.html#math_toolkit.dist.dist_ref.dists.beta_dist.references">References</a>
</h5>
<p>
@@ -625,7 +624,7 @@ from presumed-known mean and variance.
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="bernoulli_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="binomial_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="bernoulli_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="binomial_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Binomial Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="beta_dist.html" title="Beta Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="beta_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="cauchy_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="beta_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="cauchy_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist"></a><a class="link" href="binomial_dist.html" title="Binomial Distribution">
Binomial Distribution</a>
@@ -96,7 +96,7 @@
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../../doc/html/images/note.png"></td>
<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>
@@ -131,7 +131,7 @@
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/html/images/caution.png"></td>
<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">
@@ -167,12 +167,12 @@
<p>
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.member_functions"></a><h5>
<a name="id888521"></a>
<a name="id858173"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.member_functions">Member
Functions</a>
</h5>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.construct"></a><h6>
<a name="id888539"></a>
<a name="id858194"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.construct">Construct</a>
</h6>
<pre class="programlisting"><span class="identifier">binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">n</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
@@ -189,7 +189,7 @@
otherwise calls <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accessors"></a><h6>
<a name="id888657"></a>
<a name="id858336"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accessors">Accessors</a>
</h6>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
@@ -205,7 +205,7 @@
was constructed.
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction"></a><h6>
<a name="id888737"></a>
<a name="id858439"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.lower_bound_on_the_success_fraction">Lower
Bound on the Success Fraction</a>
</h6>
@@ -223,23 +223,23 @@
<dl>
<dt><span class="term">trials</span></dt>
<dd><p>
The total number of trials conducted.
</p></dd>
The total number of trials conducted.
</p></dd>
<dt><span class="term">successes</span></dt>
<dd><p>
The number of successes that occurred.
</p></dd>
The number of successes that occurred.
</p></dd>
<dt><span class="term">alpha</span></dt>
<dd><p>
The largest acceptable probability that the true value of the success
fraction is <span class="bold"><strong>less than</strong></span> the value
returned.
</p></dd>
The largest acceptable probability that the true value of the success
fraction is <span class="bold"><strong>less than</strong></span> the value
returned.
</p></dd>
<dt><span class="term">method</span></dt>
<dd><p>
An optional parameter that specifies the method to be used to compute
the interval (See below).
</p></dd>
An optional parameter that specifies the method to be used to compute
the interval (See below).
</p></dd>
</dl>
</div>
<p>
@@ -311,7 +311,7 @@
limits illustrated in the case of the binomial. Biometrika 26 404-413.
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.upper_bound_on_the_success_fraction"></a><h6>
<a name="id889186"></a>
<a name="id859008"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.upper_bound_on_the_success_fraction">Upper
Bound on the Success Fraction</a>
</h6>
@@ -329,24 +329,24 @@
<dl>
<dt><span class="term">trials</span></dt>
<dd><p>
The total number of trials conducted.
</p></dd>
The total number of trials conducted.
</p></dd>
<dt><span class="term">successes</span></dt>
<dd><p>
The number of successes that occurred.
</p></dd>
The number of successes that occurred.
</p></dd>
<dt><span class="term">alpha</span></dt>
<dd><p>
The largest acceptable probability that the true value of the success
fraction is <span class="bold"><strong>greater than</strong></span> the value
returned.
</p></dd>
The largest acceptable probability that the true value of the success
fraction is <span class="bold"><strong>greater than</strong></span> the value
returned.
</p></dd>
<dt><span class="term">method</span></dt>
<dd><p>
An optional parameter that specifies the method to be used to compute
the interval. Refer to the documentation for <code class="computeroutput"><span class="identifier">find_upper_bound_on_p</span></code>
above for the meaning of the method options.
</p></dd>
An optional parameter that specifies the method to be used to compute
the interval. Refer to the documentation for <code class="computeroutput"><span class="identifier">find_upper_bound_on_p</span></code>
above for the meaning of the method options.
</p></dd>
</dl>
</div>
<p>
@@ -364,7 +364,7 @@
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../../doc/html/images/note.png"></td>
<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">
@@ -389,7 +389,7 @@
</td></tr>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_number_of_trials_required_for_a_certain_number_of_successes"></a><h6>
<a name="id889497"></a>
<a name="id859402"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_number_of_trials_required_for_a_certain_number_of_successes">Estimating
the Number of Trials Required for a Certain Number of Successes</a>
</h6>
@@ -408,17 +408,17 @@
<dl>
<dt><span class="term">k</span></dt>
<dd><p>
The number of success observed.
</p></dd>
The number of success observed.
</p></dd>
<dt><span class="term">p</span></dt>
<dd><p>
The probability of success for each trial.
</p></dd>
The probability of success for each trial.
</p></dd>
<dt><span class="term">alpha</span></dt>
<dd><p>
The maximum acceptable probability that k events or fewer will be
observed.
</p></dd>
The maximum acceptable probability that k events or fewer will
be observed.
</p></dd>
</dl>
</div>
<p>
@@ -431,7 +431,7 @@
of seeing 10 events that occur with frequency one half.
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_maximum_number_of_trials_to_ensure_no_more_than_a_certain_number_of_successes"></a><h6>
<a name="id889696"></a>
<a name="id859651"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.estimating_the_maximum_number_of_trials_to_ensure_no_more_than_a_certain_number_of_successes">Estimating
the Maximum Number of Trials to Ensure no more than a Certain Number
of Successes</a>
@@ -451,17 +451,17 @@
<dl>
<dt><span class="term">k</span></dt>
<dd><p>
The number of success observed.
</p></dd>
The number of success observed.
</p></dd>
<dt><span class="term">p</span></dt>
<dd><p>
The probability of success for each trial.
</p></dd>
The probability of success for each trial.
</p></dd>
<dt><span class="term">alpha</span></dt>
<dd><p>
The maximum acceptable probability that more than k events will be
observed.
</p></dd>
The maximum acceptable probability that more than k events will
be observed.
</p></dd>
</dl>
</div>
<p>
@@ -479,7 +479,7 @@
Worked Example.</a>
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors"></a><h5>
<a name="id889904"></a>
<a name="id859910"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -504,7 +504,7 @@
in the context of this distribution:
</p>
<div class="table">
<a name="id890036"></a><p class="title"><b>Table&#160;11.&#160;Meaning of the non-member accessors</b></p>
<a name="id860098"></a><p class="title"><b>Table&#160;11.&#160;Meaning of the non-member accessors</b></p>
<div class="table-contents"><table class="table" summary="Meaning of the non-member accessors">
<colgroup>
<col>
@@ -512,122 +512,123 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
</th>
<p>
Function
</p>
</th>
<th>
<p>
Meaning
</p>
</th>
<p>
Meaning
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>
</p>
</td>
<p>
<a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>
</p>
</td>
<td>
<p>
The probability of obtaining <span class="bold"><strong>exactly k successes</strong></span>
from n trials with success fraction p. For example:
</p>
<p>
<code class="computeroutput"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
<span class="identifier">p</span><span class="special">),</span>
<span class="identifier">k</span><span class="special">)</span></code>
</p>
</td>
<p>
The probability of obtaining <span class="bold"><strong>exactly
k successes</strong></span> from n trials with success fraction
p. For example:
</p>
<p>
<code class="computeroutput"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
<span class="identifier">p</span><span class="special">),</span>
<span class="identifier">k</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>
</p>
</td>
<p>
<a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>
</p>
</td>
<td>
<p>
The probability of obtaining <span class="bold"><strong>k successes
or fewer</strong></span> from n trials with success fraction p. For
example:
</p>
<p>
<code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
<span class="identifier">p</span><span class="special">),</span>
<span class="identifier">k</span><span class="special">)</span></code>
</p>
</td>
<p>
The probability of obtaining <span class="bold"><strong>k successes
or fewer</strong></span> from n trials with success fraction p.
For example:
</p>
<p>
<code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
<span class="identifier">p</span><span class="special">),</span>
<span class="identifier">k</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../nmp.html#math.dist.ccdf">Complement of the Cumulative Distribution
Function</a>
</p>
</td>
<p>
<a class="link" href="../nmp.html#math.dist.ccdf">Complement of the Cumulative
Distribution Function</a>
</p>
</td>
<td>
<p>
The probability of obtaining <span class="bold"><strong>more than k
successes</strong></span> from n trials with success fraction p. For
example:
</p>
<p>
<code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
<span class="identifier">p</span><span class="special">),</span>
<span class="identifier">k</span><span class="special">))</span></code>
</p>
</td>
<p>
The probability of obtaining <span class="bold"><strong>more than
k successes</strong></span> from n trials with success fraction
p. For example:
</p>
<p>
<code class="computeroutput"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
<span class="identifier">p</span><span class="special">),</span>
<span class="identifier">k</span><span class="special">))</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>
</p>
</td>
<p>
<a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>
</p>
</td>
<td>
<p>
The <span class="bold"><strong>greatest</strong></span> number of successes
that may be observed from n trials with success fraction p, at
probability P. Note that the value returned is a real-number, and
not an integer. Depending on the use case you may want to take
either the floor or ceiling of the result. For example:
</p>
<p>
<code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
<span class="identifier">p</span><span class="special">),</span>
<span class="identifier">P</span><span class="special">)</span></code>
</p>
</td>
<p>
The <span class="bold"><strong>greatest</strong></span> number of successes
that may be observed from n trials with success fraction p,
at probability P. Note that the value returned is a real-number,
and not an integer. Depending on the use case you may want
to take either the floor or ceiling of the result. For example:
</p>
<p>
<code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
<span class="identifier">p</span><span class="special">),</span>
<span class="identifier">P</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../nmp.html#math.dist.quantile_c">Quantile from the complement
of the probability</a>
</p>
</td>
<p>
<a class="link" href="../nmp.html#math.dist.quantile_c">Quantile from the complement
of the probability</a>
</p>
</td>
<td>
<p>
The <span class="bold"><strong>smallest</strong></span> number of successes
that may be observed from n trials with success fraction p, at
probability P. Note that the value returned is a real-number, and
not an integer. Depending on the use case you may want to take
either the floor or ceiling of the result. For example:
</p>
<p>
<code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
<span class="identifier">p</span><span class="special">),</span>
<span class="identifier">P</span><span class="special">))</span></code>`
</p>
</td>
<p>
The <span class="bold"><strong>smallest</strong></span> number of successes
that may be observed from n trials with success fraction p,
at probability P. Note that the value returned is a real-number,
and not an integer. Depending on the use case you may want
to take either the floor or ceiling of the result. For example:
</p>
<p>
<code class="computeroutput"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">binomial</span><span class="special">(</span><span class="identifier">n</span><span class="special">,</span>
<span class="identifier">p</span><span class="special">),</span>
<span class="identifier">P</span><span class="special">))</span></code>`
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><a name="math_toolkit.dist.dist_ref.dists.binomial_dist.examples"></a><h5>
<a name="id890451"></a>
<a name="id860601"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.examples">Examples</a>
</h5>
<p>
@@ -635,7 +636,7 @@
examples</a> are available illustrating the use of the binomial distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy"></a><h5>
<a name="id890472"></a>
<a name="id860637"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -645,7 +646,7 @@
please refer to these functions for information on accuracy.
</p>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.implementation"></a><h5>
<a name="id891904"></a>
<a name="id860680"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.implementation">Implementation</a>
</h5>
<p>
@@ -661,248 +662,251 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Implementation is in terms of <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>:
if <sub>n</sub>C<sub>k </sub> is the binomial coefficient of a and b, then we have:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/binomial_ref1.png"></span>
</p>
<p>
Which can be evaluated as <code class="computeroutput"><span class="identifier">ibeta_derivative</span><span class="special">(</span><span class="identifier">k</span><span class="special">+</span><span class="number">1</span><span class="special">,</span> <span class="identifier">n</span><span class="special">-</span><span class="identifier">k</span><span class="special">+</span><span class="number">1</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
<span class="special">(</span><span class="identifier">n</span><span class="special">+</span><span class="number">1</span><span class="special">)</span></code>
</p>
<p>
The function <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>
is used here, since it has already been optimised for the lowest
possible error - indeed this is really just a thin wrapper around
part of the internals of the incomplete beta function.
</p>
<p>
There are also various special cases: refer to the code for details.
</p>
<p>
Implementation is in terms of <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>:
if <sub>n</sub>C<sub>k </sub> is the binomial coefficient of a and b, then we have:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/binomial_ref1.png"></span>
</p>
<p>
Which can be evaluated as <code class="computeroutput"><span class="identifier">ibeta_derivative</span><span class="special">(</span><span class="identifier">k</span><span class="special">+</span><span class="number">1</span><span class="special">,</span> <span class="identifier">n</span><span class="special">-</span><span class="identifier">k</span><span class="special">+</span><span class="number">1</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
<span class="special">(</span><span class="identifier">n</span><span class="special">+</span><span class="number">1</span><span class="special">)</span></code>
</p>
<p>
The function <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>
is used here, since it has already been optimised for the lowest
possible error - indeed this is really just a thin wrapper
around part of the internals of the incomplete beta function.
</p>
<p>
There are also various special cases: refer to the code for
details.
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
<p>
Using the relation:
</p>
<p>
</p>
<pre xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="table-programlisting"><span class="identifier">p</span> <span class="special">=</span> <span class="identifier">I</span><span class="special">[</span><span class="identifier">sub</span> <span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">](</span><span class="identifier">n</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">k</span> <span class="special">+</span> <span class="number">1</span><span class="special">)</span>
<span class="special">=</span> <span class="number">1</span> <span class="special">-</span> <span class="identifier">I</span><span class="special">[</span><span class="identifier">sub</span> <span class="identifier">p</span><span class="special">](</span><span class="identifier">k</span> <span class="special">+</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">n</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">)</span>
<span class="special">=</span> <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a><span class="special">(</span><span class="identifier">k</span> <span class="special">+</span> <span class="number">1</span><span class="special">,</span> <span class="identifier">n</span> <span class="special">-</span> <span class="identifier">k</span><span class="special">,</span> <span class="identifier">p</span><span class="special">)</span></pre>
<p>
</p>
<p>
There are also various special cases: refer to the code for details.
</p>
</p>
<p>
There are also various special cases: refer to the code for
details.
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(k
+ 1, n - k, p)
</p>
<p>
There are also various special cases: refer to the code for details.
</p>
<p>
Using the relation: q = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(k
+ 1, n - k, p)
</p>
<p>
There are also various special cases: refer to the code for
details.
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Since the cdf is non-linear in variate <span class="emphasis"><em>k</em></span>
none of the inverse incomplete beta functions can be used here.
Instead the quantile is found numerically using a derivative
free method (<a class="link" href="../../../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">TOMS
Algorithm 748</a>).
</p>
<p>
Since the cdf is non-linear in variate <span class="emphasis"><em>k</em></span>
none of the inverse incomplete beta functions can be used here.
Instead the quantile is found numerically using a derivative
free method (<a class="link" href="../../../toolkit/internals1/roots2.html" title="Root Finding Without Derivatives">TOMS
Algorithm 748</a>).
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Found numerically as above.
</p>
<p>
Found numerically as above.
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">p</span> <span class="special">*</span>
<span class="identifier">n</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">p</span> <span class="special">*</span>
<span class="identifier">n</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">p</span> <span class="special">*</span>
<span class="identifier">n</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">)</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">p</span> <span class="special">*</span>
<span class="identifier">n</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">p</span> <span class="special">*</span>
<span class="special">(</span><span class="identifier">n</span>
<span class="special">+</span> <span class="number">1</span><span class="special">))</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">floor</span><span class="special">(</span><span class="identifier">p</span> <span class="special">*</span>
<span class="special">(</span><span class="identifier">n</span>
<span class="special">+</span> <span class="number">1</span><span class="special">))</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="number">2</span>
<span class="special">*</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
<span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">n</span> <span class="special">*</span>
<span class="identifier">p</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">p</span><span class="special">))</span></code>
</p>
<p>
<code class="computeroutput"><span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="number">2</span>
<span class="special">*</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
<span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">n</span> <span class="special">*</span>
<span class="identifier">p</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">p</span><span class="special">))</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">3</span> <span class="special">-</span>
<span class="special">(</span><span class="number">6</span>
<span class="special">/</span> <span class="identifier">n</span><span class="special">)</span> <span class="special">+</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">/</span> <span class="special">(</span><span class="identifier">n</span> <span class="special">*</span>
<span class="identifier">p</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">p</span><span class="special">)))</span></code>
</p>
<p>
<code class="computeroutput"><span class="number">3</span> <span class="special">-</span>
<span class="special">(</span><span class="number">6</span>
<span class="special">/</span> <span class="identifier">n</span><span class="special">)</span> <span class="special">+</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">/</span> <span class="special">(</span><span class="identifier">n</span> <span class="special">*</span>
<span class="identifier">p</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">p</span><span class="special">)))</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="number">6</span>
<span class="special">*</span> <span class="identifier">p</span>
<span class="special">*</span> <span class="identifier">q</span><span class="special">)</span> <span class="special">/</span>
<span class="special">(</span><span class="identifier">n</span>
<span class="special">*</span> <span class="identifier">p</span>
<span class="special">*</span> <span class="identifier">q</span><span class="special">)</span></code>
</p>
<p>
<code class="computeroutput"><span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="number">6</span>
<span class="special">*</span> <span class="identifier">p</span>
<span class="special">*</span> <span class="identifier">q</span><span class="special">)</span> <span class="special">/</span>
<span class="special">(</span><span class="identifier">n</span>
<span class="special">*</span> <span class="identifier">p</span>
<span class="special">*</span> <span class="identifier">q</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
parameter estimation
</p>
<p>
parameter estimation
</p>
</td>
<td>
<p>
The member functions <code class="computeroutput"><span class="identifier">find_upper_bound_on_p</span></code>
<code class="computeroutput"><span class="identifier">find_lower_bound_on_p</span></code>
and <code class="computeroutput"><span class="identifier">find_number_of_trials</span></code>
are implemented in terms of the inverse incomplete beta functions
<a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>,
<a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>,
and <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a>
respectively
</p>
<p>
The member functions <code class="computeroutput"><span class="identifier">find_upper_bound_on_p</span></code>
<code class="computeroutput"><span class="identifier">find_lower_bound_on_p</span></code>
and <code class="computeroutput"><span class="identifier">find_number_of_trials</span></code>
are implemented in terms of the inverse incomplete beta functions
<a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>,
<a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>,
and <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_invb</a>
respectively
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.binomial_dist.references"></a><h5>
<a name="id892937"></a>
<a name="id861884"></a>
<a class="link" href="binomial_dist.html#math_toolkit.dist.dist_ref.dists.binomial_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li>
<a href="http://mathworld.wolfram.com/BinomialDistribution.html" target="_top">Weisstein,
Eric W. "Binomial Distribution." From MathWorld--A Wolfram
Web Resource</a>.
</li>
<li>
<a href="http://en.wikipedia.org/wiki/Beta_distribution" target="_top">Wikipedia
binomial distribution</a>.
</li>
<li>
<a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda366i.htm" target="_top">NIST
Explorary Data Analysis</a>.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a href="http://mathworld.wolfram.com/BinomialDistribution.html" target="_top">Weisstein,
Eric W. "Binomial Distribution." From MathWorld--A Wolfram
Web Resource</a>.
</li>
<li class="listitem">
<a href="http://en.wikipedia.org/wiki/Beta_distribution" target="_top">Wikipedia
binomial distribution</a>.
</li>
<li class="listitem">
<a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda366i.htm" target="_top">NIST
Explorary Data Analysis</a>.
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -917,7 +921,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="beta_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="cauchy_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="beta_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="cauchy_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Cauchy-Lorentz Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="binomial_dist.html" title="Binomial Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="binomial_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="chi_squared_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="binomial_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="chi_squared_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist"></a><a class="link" href="cauchy_dist.html" title="Cauchy-Lorentz Distribution"> Cauchy-Lorentz
Distribution</a>
@@ -88,7 +88,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/cauchy_pdf2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions"></a><h5>
<a name="id893445"></a>
<a name="id862513"></a>
<a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.member_functions">Member
Functions</a>
</h5>
@@ -114,7 +114,7 @@
Returns the scale parameter of the distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors"></a><h5>
<a name="id893592"></a>
<a name="id862699"></a>
<a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -133,11 +133,8 @@
<p>
Note however that the Cauchy distribution does not have a mean, standard
deviation, etc. See <a class="link" href="../../../policy/pol_ref/assert_undefined.html" title="Mathematically Undefined Function Policies">mathematically
undefined function</a>
</p>
<p>
to control whether these should fail to compile with a BOOST_STATIC_ASSERTION_FAILURE,
which is the default.
undefined function</a> to control whether these should fail to compile
with a BOOST_STATIC_ASSERTION_FAILURE, which is the default.
</p>
<p>
Alternately, the functions <a class="link" href="../nmp.html#math.dist.mean">mean</a>,
@@ -151,7 +148,7 @@
The domain of the random variable is [-[max_value], +[min_value]].
</p>
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy"></a><h5>
<a name="id893739"></a>
<a name="id862918"></a>
<a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -160,7 +157,7 @@
have very low error rates.
</p>
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation"></a><h5>
<a name="id893772"></a>
<a name="id862968"></a>
<a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.implementation">Implementation</a>
</h5>
<p>
@@ -175,118 +172,124 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = 1 / (&#960; * &#947; * (1 + ((x - x<sub>0 </sub>) / &#947;)<sup>2</sup>)
</p>
<p>
Using the relation: pdf = 1 / (&#960; * &#947; * (1 + ((x - x<sub>0 </sub>) / &#947;)<sup>2</sup>)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf and its complement
</p>
<p>
cdf and its complement
</p>
</td>
<td>
<p>
The cdf is normally given by:
</p>
<p>
p = 0.5 + atan(x)/&#960;
</p>
<p>
But that suffers from cancellation error as x -&gt; -&#8734;. So recall
that for <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;</span>
<span class="number">0</span></code>:
</p>
<p>
atan(x) = -&#960;/2 - atan(1/x)
</p>
<p>
Substituting into the above we get:
</p>
<p>
p = -atan(1/x) ; x &lt; 0
</p>
<p>
So the procedure is to calculate the cdf for -fabs(x) using the
above formula. Note that to factor in the location and scale
parameters you must substitute (x - x<sub>0 </sub>) / &#947; for x in the above.
</p>
<p>
This procedure yields the smaller of <span class="emphasis"><em>p</em></span> and
<span class="emphasis"><em>q</em></span>, so the result may need subtracting from
1 depending on whether we want the complement or not, and whether
<span class="emphasis"><em>x</em></span> is less than x<sub>0 </sub> or not.
</p>
<p>
The cdf is normally given by:
</p>
<p>
p = 0.5 + atan(x)/&#960;
</p>
<p>
But that suffers from cancellation error as x -&gt; -&#8734;. So recall
that for <code class="computeroutput"><span class="identifier">x</span> <span class="special">&lt;</span> <span class="number">0</span></code>:
</p>
<p>
atan(x) = -&#960;/2 - atan(1/x)
</p>
<p>
Substituting into the above we get:
</p>
<p>
p = -atan(1/x) ; x &lt; 0
</p>
<p>
So the procedure is to calculate the cdf for -fabs(x) using
the above formula. Note that to factor in the location and
scale parameters you must substitute (x - x<sub>0 </sub>) / &#947; for x in the
above.
</p>
<p>
This procedure yields the smaller of <span class="emphasis"><em>p</em></span>
and <span class="emphasis"><em>q</em></span>, so the result may need subtracting
from 1 depending on whether we want the complement or not,
and whether <span class="emphasis"><em>x</em></span> is less than x<sub>0 </sub> or not.
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
The same procedure is used irrespective of whether we're starting
from the probability or it's complement. First the argument
<span class="emphasis"><em>p</em></span> is reduced to the range [-0.5, 0.5], then
the relation
</p>
<p>
x = x<sub>0 </sub> &#177; &#947; / tan(&#960; * p)
</p>
<p>
is used to obtain the result. Whether we're adding or subtracting
from x<sub>0 </sub> is determined by whether we're starting from the complement
or not.
</p>
<p>
The same procedure is used irrespective of whether we're starting
from the probability or it's complement. First the argument
<span class="emphasis"><em>p</em></span> is reduced to the range [-0.5, 0.5],
then the relation
</p>
<p>
x = x<sub>0 </sub> &#177; &#947; / tan(&#960; * p)
</p>
<p>
is used to obtain the result. Whether we're adding or subtracting
from x<sub>0 </sub> is determined by whether we're starting from the complement
or not.
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
The location parameter.
</p>
<p>
The location parameter.
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.cauchy_dist.references"></a><h5>
<a name="id893997"></a>
<a name="id863237"></a>
<a class="link" href="cauchy_dist.html#math_toolkit.dist.dist_ref.dists.cauchy_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li><a href="http://en.wikipedia.org/wiki/Cauchy_distribution" target="_top">Cauchy-Lorentz
distribution</a></li>
<li><a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm" target="_top">NIST
Exploratory Data Analysis</a></li>
<li><a href="http://mathworld.wolfram.com/CauchyDistribution.html" target="_top">Weisstein,
Eric W. "Cauchy Distribution." From MathWorld--A Wolfram
Web Resource.</a></li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a href="http://en.wikipedia.org/wiki/Cauchy_distribution" target="_top">Cauchy-Lorentz
distribution</a>
</li>
<li class="listitem">
<a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3663.htm" target="_top">NIST
Exploratory Data Analysis</a>
</li>
<li class="listitem">
<a href="http://mathworld.wolfram.com/CauchyDistribution.html" target="_top">Weisstein,
Eric W. "Cauchy Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -301,7 +304,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="binomial_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="chi_squared_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Chi Squared Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
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@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="cauchy_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="exp_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist"></a><a class="link" href="chi_squared_dist.html" title="Chi Squared Distribution">
Chi Squared Distribution</a>
@@ -87,7 +87,7 @@ independent, normally distributed random
<span class="inlinemediaobject"><img src="../../../../../graphs/chi_squared_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions"></a><h5>
<a name="id894640"></a>
<a name="id863884"></a>
<a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.member_functions">Member
Functions</a>
</h5>
@@ -122,28 +122,28 @@ independent, normally distributed random
<dl>
<dt><span class="term">difference_from_variance</span></dt>
<dd><p>
The difference from the assumed nominal variance that is to be detected:
Note that the sign of this value is critical, see below.
</p></dd>
The difference from the assumed nominal variance that is to be
detected: Note that the sign of this value is critical, see below.
</p></dd>
<dt><span class="term">alpha</span></dt>
<dd><p>
The maximum acceptable risk of rejecting the null hypothesis when
it is in fact true.
</p></dd>
The maximum acceptable risk of rejecting the null hypothesis when
it is in fact true.
</p></dd>
<dt><span class="term">beta</span></dt>
<dd><p>
The maximum acceptable risk of falsely failing to reject the null
hypothesis.
</p></dd>
The maximum acceptable risk of falsely failing to reject the null
hypothesis.
</p></dd>
<dt><span class="term">variance</span></dt>
<dd><p>
The nominal variance being tested against.
</p></dd>
The nominal variance being tested against.
</p></dd>
<dt><span class="term">hint</span></dt>
<dd><p>
An optional hint on where to start looking for a result: the current
sample size would be a good choice.
</p></dd>
An optional hint on where to start looking for a result: the current
sample size would be a good choice.
</p></dd>
</dl>
</div>
<p>
@@ -170,7 +170,7 @@ independent, normally distributed random
NIST Engineering Statistics Handbook, Section 7.2.3.2</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.non_member_accessors"></a><h5>
<a name="id894965"></a>
<a name="id864324"></a>
<a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -196,7 +196,7 @@ independent, normally distributed random
The domain of the random variable is [0, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples"></a><h5>
<a name="id895068"></a>
<a name="id864476"></a>
<a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.examples">Examples</a>
</h5>
<p>
@@ -204,7 +204,7 @@ independent, normally distributed random
are available illustrating the use of the Chi Squared Distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy"></a><h5>
<a name="id895094"></a>
<a name="id864510"></a>
<a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -212,7 +212,7 @@ independent, normally distributed random
gamma functions</a>: please refer to the accuracy data for those functions.
</p>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation"></a><h5>
<a name="id895118"></a>
<a name="id864549"></a>
<a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.implementation">Implementation</a>
</h5>
<p>
@@ -228,168 +228,174 @@ independent, normally distributed random
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = <a class="link" href="../../../special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">gamma_p_derivative</a>(v
/ 2, x / 2) / 2
</p>
<p>
Using the relation: pdf = <a class="link" href="../../../special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">gamma_p_derivative</a>(v
/ 2, x / 2) / 2
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: p = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>(v
/ 2, x / 2)
</p>
<p>
Using the relation: p = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>(v
/ 2, x / 2)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>(v
/ 2, x / 2)
</p>
<p>
Using the relation: q = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>(v
/ 2, x / 2)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: x = 2 * <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>(v
/ 2, p)
</p>
<p>
Using the relation: x = 2 * <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>(v
/ 2, p)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: x = 2 * <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>(v
/ 2, p)
</p>
<p>
Using the relation: x = 2 * <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>(v
/ 2, p)
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
v
</p>
<p>
v
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
2v
</p>
<p>
2v
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
v - 2 (if v &gt;= 2)
</p>
<p>
v - 2 (if v &gt;= 2)
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
2 * sqrt(2 / v) == sqrt(8 / v)
</p>
<p>
2 * sqrt(2 / v) == sqrt(8 / v)
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
3 + 12 / v
</p>
<p>
3 + 12 / v
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
12 / v
</p>
<p>
12 / v
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.chi_squared_dist.references"></a><h5>
<a name="id895397"></a>
<a name="id864870"></a>
<a class="link" href="chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.chi_squared_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li><a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm" target="_top">NIST
Exploratory Data Analysis</a></li>
<li><a href="http://en.wikipedia.org/wiki/Chi-square_distribution" target="_top">Chi-square
distribution</a></li>
<li><a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html" target="_top">Weisstein,
Eric W. "Chi-Squared Distribution." From MathWorld--A Wolfram
Web Resource.</a></li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm" target="_top">NIST
Exploratory Data Analysis</a>
</li>
<li class="listitem">
<a href="http://en.wikipedia.org/wiki/Chi-square_distribution" target="_top">Chi-square
distribution</a>
</li>
<li class="listitem">
<a href="http://mathworld.wolfram.com/Chi-SquaredDistribution.html" target="_top">Weisstein,
Eric W. "Chi-Squared Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -404,7 +410,7 @@ independent, normally distributed random
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="cauchy_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="exp_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="cauchy_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="exp_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Exponential Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="chi_squared_dist.html" title="Chi Squared Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="chi_squared_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="extreme_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="chi_squared_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="extreme_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.exp_dist"></a><a class="link" href="exp_dist.html" title="Exponential Distribution"> Exponential
Distribution</a>
@@ -71,7 +71,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/exponential_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.member_functions"></a><h5>
<a name="id895820"></a>
<a name="id865397"></a>
<a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.member_functions">Member
Functions</a>
</h5>
@@ -91,7 +91,7 @@
Accessor function returns the lambda parameter of the distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors"></a><h5>
<a name="id895921"></a>
<a name="id865522"></a>
<a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -111,7 +111,7 @@
The domain of the random variable is [0, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.accuracy"></a><h5>
<a name="id896021"></a>
<a name="id865670"></a>
<a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -122,7 +122,7 @@
should have very low error rates.
</p>
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.implementation"></a><h5>
<a name="id896069"></a>
<a name="id865741"></a>
<a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.implementation">Implementation</a>
</h5>
<p>
@@ -137,176 +137,184 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = &#955; * exp(-&#955; * x)
</p>
<p>
Using the relation: pdf = &#955; * exp(-&#955; * x)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: p = 1 - exp(-x * &#955;) = -expm1(-x * &#955;)
</p>
<p>
Using the relation: p = 1 - exp(-x * &#955;) = -expm1(-x * &#955;)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = exp(-x * &#955;)
</p>
<p>
Using the relation: q = exp(-x * &#955;)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: x = -log(1-p) / &#955; = -log1p(-p) / &#955;
</p>
<p>
Using the relation: x = -log(1-p) / &#955; = -log1p(-p) / &#955;
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: x = -log(q) / &#955;
</p>
<p>
Using the relation: x = -log(q) / &#955;
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
1/&#955;
</p>
<p>
1/&#955;
</p>
</td>
</tr>
<tr>
<td>
<p>
standard deviation
</p>
<p>
standard deviation
</p>
</td>
<td>
<p>
1/&#955;
</p>
<p>
1/&#955;
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
0
</p>
<p>
0
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
2
</p>
<p>
2
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
9
</p>
<p>
9
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
6
</p>
<p>
6
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.exp_dist.references"></a><h5>
<a name="id896320"></a>
<a name="id866026"></a>
<a class="link" href="exp_dist.html#math_toolkit.dist.dist_ref.dists.exp_dist.references">references</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li><a href="http://mathworld.wolfram.com/ExponentialDistribution.html" target="_top">Weisstein,
Eric W. "Exponential Distribution." From MathWorld--A Wolfram
Web Resource</a></li>
<li><a href="http://documents.wolfram.com/calccenter/Functions/ListsMatrices/Statistics/ExponentialDistribution.html" target="_top">Wolfram
Mathematica calculator</a></li>
<li><a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3667.htm" target="_top">NIST
Exploratory Data Analysis</a></li>
<li><a href="http://en.wikipedia.org/wiki/Exponential_distribution" target="_top">Wikipedia
Exponential distribution</a></li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a href="http://mathworld.wolfram.com/ExponentialDistribution.html" target="_top">Weisstein,
Eric W. "Exponential Distribution." From MathWorld--A Wolfram
Web Resource</a>
</li>
<li class="listitem">
<a href="http://documents.wolfram.com/calccenter/Functions/ListsMatrices/Statistics/ExponentialDistribution.html" target="_top">Wolfram
Mathematica calculator</a>
</li>
<li class="listitem">
<a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3667.htm" target="_top">NIST
Exploratory Data Analysis</a>
</li>
<li class="listitem">
<a href="http://en.wikipedia.org/wiki/Exponential_distribution" target="_top">Wikipedia
Exponential distribution</a>
</li>
</ul></div>
<p>
(See also the reference documentation for the related <a class="link" href="extreme_dist.html" title="Extreme Value Distribution">Extreme
Distributions</a>.)
</p>
<div class="itemizedlist"><ul type="disc"><li>
<a href="http://www.worldscibooks.com/mathematics/p191.html" target="_top">Extreme
Value Distributions, Theory and Applications Samuel Kotz &amp; Saralees
Nadarajah</a> discuss the relationship of the types of extreme
value distributions.
</li></ul></div>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
<a href="http://www.worldscibooks.com/mathematics/p191.html" target="_top">Extreme
Value Distributions, Theory and Applications Samuel Kotz &amp; Saralees
Nadarajah</a> discuss the relationship of the types of extreme
value distributions.
</li></ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
@@ -320,7 +328,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="chi_squared_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="extreme_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="chi_squared_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="extreme_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Extreme Value Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="exp_dist.html" title="Exponential Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="exp_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="f_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="exp_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="f_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist"></a><a class="link" href="extreme_dist.html" title="Extreme Value Distribution"> Extreme
Value Distribution</a>
@@ -100,7 +100,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/extreme_value_pdf2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions"></a><h5>
<a name="id897027"></a>
<a name="id866599"></a>
<a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.member_functions">Member
Functions</a>
</h5>
@@ -125,7 +125,7 @@
Returns the scale parameter of the distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors"></a><h5>
<a name="id897183"></a>
<a name="id866916"></a>
<a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -145,7 +145,7 @@
The domain of the random parameter is [-&#8734;, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy"></a><h5>
<a name="id897280"></a>
<a name="id867064"></a>
<a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -154,7 +154,7 @@
very low error rates.
</p>
<a name="math_toolkit.dist.dist_ref.dists.extreme_dist.implementation"></a><h5>
<a name="id897314"></a>
<a name="id867112"></a>
<a class="link" href="extreme_dist.html#math_toolkit.dist.dist_ref.dists.extreme_dist.implementation">Implementation</a>
</h5>
<p>
@@ -170,149 +170,149 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = exp((a-x)/b) * exp(-exp((a-x)/b)) /
b
</p>
<p>
Using the relation: pdf = exp((a-x)/b) * exp(-exp((a-x)/b))
/ b
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: p = exp(-exp((a-x)/b))
</p>
<p>
Using the relation: p = exp(-exp((a-x)/b))
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = -expm1(-exp((a-x)/b))
</p>
<p>
Using the relation: q = -expm1(-exp((a-x)/b))
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: a - log(-log(p)) * b
</p>
<p>
Using the relation: a - log(-log(p)) * b
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: a - log(-log1p(-q)) * b
</p>
<p>
Using the relation: a - log(-log1p(-q)) * b
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
a + <a href="http://en.wikipedia.org/wiki/Euler-Mascheroni_constant" target="_top">Euler-Mascheroni-constant</a>
* b
</p>
<p>
a + <a href="http://en.wikipedia.org/wiki/Euler-Mascheroni_constant" target="_top">Euler-Mascheroni-constant</a>
* b
</p>
</td>
</tr>
<tr>
<td>
<p>
standard deviation
</p>
<p>
standard deviation
</p>
</td>
<td>
<p>
pi * b / sqrt(6)
</p>
<p>
pi * b / sqrt(6)
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
The same as the location parameter <span class="emphasis"><em>a</em></span>.
</p>
<p>
The same as the location parameter <span class="emphasis"><em>a</em></span>.
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
12 * sqrt(6) * zeta(3) / pi<sup>3</sup>
</p>
<p>
12 * sqrt(6) * zeta(3) / pi<sup>3</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
27 / 5
</p>
<p>
27 / 5
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
kurtosis - 3 or 12 / 5
</p>
<p>
kurtosis - 3 or 12 / 5
</p>
</td>
</tr>
</tbody>
@@ -330,7 +330,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="exp_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="f_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>F Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="extreme_dist.html" title="Extreme Value Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="extreme_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="gamma_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="extreme_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="gamma_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.f_dist"></a><a class="link" href="f_dist.html" title="F Distribution"> F Distribution</a>
</h5></div></div></div>
@@ -80,7 +80,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/fisher_f_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.f_dist.member_functions"></a><h5>
<a name="id898063"></a>
<a name="id867979"></a>
<a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.member_functions">Member
Functions</a>
</h5>
@@ -106,7 +106,7 @@
Returns the denominator degrees of freedom parameter of the distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors"></a><h5>
<a name="id898216"></a>
<a name="id868168"></a>
<a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -126,7 +126,7 @@
The domain of the random variable is [0, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.f_dist.examples"></a><h5>
<a name="id898316"></a>
<a name="id868317"></a>
<a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.examples">Examples</a>
</h5>
<p>
@@ -134,7 +134,7 @@
are available illustrating the use of the F Distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.f_dist.accuracy"></a><h5>
<a name="id898337"></a>
<a name="id868352"></a>
<a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -143,7 +143,7 @@
refer to those functions for accuracy data.
</p>
<a name="math_toolkit.dist.dist_ref.dists.f_dist.implementation"></a><h5>
<a name="id898364"></a>
<a name="id868397"></a>
<a class="link" href="f_dist.html#math_toolkit.dist.dist_ref.dists.f_dist.implementation">Implementation</a>
</h5>
<p>
@@ -159,263 +159,267 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
The usual form of the PDF is given by:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/fisher_pdf.png"></span>
</p>
<p>
However, that form is hard to evaluate directly without incurring
problems with either accuracy or numeric overflow.
</p>
<p>
Direct differentiation of the CDF expressed in terms of the incomplete
beta function
</p>
<p>
led to the following two formulas:
</p>
<p>
f<sub>v1,v2</sub>(x) = y * <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>(v2
/ 2, v1 / 2, v2 / (v2 + v1 * x))
</p>
<p>
with y = (v2 * v1) / ((v2 + v1 * x) * (v2 + v1 * x))
</p>
<p>
and
</p>
<p>
f<sub>v1,v2</sub>(x) = y * <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>(v1
/ 2, v2 / 2, v1 * x / (v2 + v1 * x))
</p>
<p>
with y = (z * v1 - x * v1 * v1) / z<sup>2</sup>
</p>
<p>
and z = v2 + v1 * x
</p>
<p>
The first of these is used for v1 * x &gt; v2, otherwise the
second is used.
</p>
<p>
The aim is to keep the <span class="emphasis"><em>x</em></span> argument to <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>
away from 1 to avoid rounding error.
</p>
<p>
The usual form of the PDF is given by:
</p>
<p>
<span class="inlinemediaobject"><img src="../../../../../equations/fisher_pdf.png"></span>
</p>
<p>
However, that form is hard to evaluate directly without incurring
problems with either accuracy or numeric overflow.
</p>
<p>
Direct differentiation of the CDF expressed in terms of the
incomplete beta function
</p>
<p>
led to the following two formulas:
</p>
<p>
f<sub>v1,v2</sub>(x) = y * <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>(v2
/ 2, v1 / 2, v2 / (v2 + v1 * x))
</p>
<p>
with y = (v2 * v1) / ((v2 + v1 * x) * (v2 + v1 * x))
</p>
<p>
and
</p>
<p>
f<sub>v1,v2</sub>(x) = y * <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>(v1
/ 2, v2 / 2, v1 * x / (v2 + v1 * x))
</p>
<p>
with y = (z * v1 - x * v1 * v1) / z<sup>2</sup>
</p>
<p>
and z = v2 + v1 * x
</p>
<p>
The first of these is used for v1 * x &gt; v2, otherwise the
second is used.
</p>
<p>
The aim is to keep the <span class="emphasis"><em>x</em></span> argument to
<a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>
away from 1 to avoid rounding error.
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relations:
</p>
<p>
p = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(v1
/ 2, v2 / 2, v1 * x / (v2 + v1 * x))
</p>
<p>
and
</p>
<p>
p = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>(v2
/ 2, v1 / 2, v2 / (v2 + v1 * x))
</p>
<p>
The first is used for v1 * x &gt; v2, otherwise the second is
used.
</p>
<p>
The aim is to keep the <span class="emphasis"><em>x</em></span> argument to <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
well away from 1 to avoid rounding error.
</p>
<p>
Using the relations:
</p>
<p>
p = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(v1
/ 2, v2 / 2, v1 * x / (v2 + v1 * x))
</p>
<p>
and
</p>
<p>
p = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>(v2
/ 2, v1 / 2, v2 / (v2 + v1 * x))
</p>
<p>
The first is used for v1 * x &gt; v2, otherwise the second
is used.
</p>
<p>
The aim is to keep the <span class="emphasis"><em>x</em></span> argument to
<a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
well away from 1 to avoid rounding error.
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relations:
</p>
<p>
p = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>(v1
/ 2, v2 / 2, v1 * x / (v2 + v1 * x))
</p>
<p>
and
</p>
<p>
p = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(v2
/ 2, v1 / 2, v2 / (v2 + v1 * x))
</p>
<p>
The first is used for v1 * x &lt; v2, otherwise the second is
used.
</p>
<p>
The aim is to keep the <span class="emphasis"><em>x</em></span> argument to <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
well away from 1 to avoid rounding error.
</p>
<p>
Using the relations:
</p>
<p>
p = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>(v1
/ 2, v2 / 2, v1 * x / (v2 + v1 * x))
</p>
<p>
and
</p>
<p>
p = <a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(v2
/ 2, v1 / 2, v2 / (v2 + v1 * x))
</p>
<p>
The first is used for v1 * x &lt; v2, otherwise the second
is used.
</p>
<p>
The aim is to keep the <span class="emphasis"><em>x</em></span> argument to
<a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>
well away from 1 to avoid rounding error.
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
x = v2 * a / (v1 * b)
</p>
<p>
where:
</p>
<p>
a = <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>(v1
/ 2, v2 / 2, p)
</p>
<p>
and
</p>
<p>
b = 1 - a
</p>
<p>
Quantities <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>
are both computed by <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
without the subtraction implied above.
</p>
<p>
Using the relation:
</p>
<p>
x = v2 * a / (v1 * b)
</p>
<p>
where:
</p>
<p>
a = <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>(v1
/ 2, v2 / 2, p)
</p>
<p>
and
</p>
<p>
b = 1 - a
</p>
<p>
Quantities <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>
are both computed by <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
without the subtraction implied above.
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
from the complement
</p>
<p>
quantile
</p>
<p>
from the complement
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
x = v2 * a / (v1 * b)
</p>
<p>
where
</p>
<p>
a = <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>(v1
/ 2, v2 / 2, p)
</p>
<p>
and
</p>
<p>
b = 1 - a
</p>
<p>
Quantities <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>
are both computed by <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>
without the subtraction implied above.
</p>
<p>
Using the relation:
</p>
<p>
x = v2 * a / (v1 * b)
</p>
<p>
where
</p>
<p>
a = <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>(v1
/ 2, v2 / 2, p)
</p>
<p>
and
</p>
<p>
b = 1 - a
</p>
<p>
Quantities <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span>
are both computed by <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibetac_inv</a>
without the subtraction implied above.
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
v2 / (v2 - 2)
</p>
<p>
v2 / (v2 - 2)
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
2 * v2<sup>2 </sup> * (v1 + v2 - 2) / (v1 * (v2 - 2) * (v2 - 2) * (v2 - 4))
</p>
<p>
2 * v2<sup>2 </sup> * (v1 + v2 - 2) / (v1 * (v2 - 2) * (v2 - 2) * (v2 -
4))
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
v2 * (v1 - 2) / (v1 * (v2 + 2))
</p>
<p>
v2 * (v1 - 2) / (v1 * (v2 + 2))
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
2 * (v2 + 2 * v1 - 2) * sqrt((2 * v2 - 8) / (v1 * (v2 + v1 -
2))) / (v2 - 6)
</p>
<p>
2 * (v2 + 2 * v1 - 2) * sqrt((2 * v2 - 8) / (v1 * (v2 + v1
- 2))) / (v2 - 6)
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis and kurtosis excess
</p>
<p>
kurtosis and kurtosis excess
</p>
</td>
<td>
<p>
Refer to, <a href="http://mathworld.wolfram.com/F-Distribution.html" target="_top">Weisstein,
Eric W. "F-Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
<p>
Refer to, <a href="http://mathworld.wolfram.com/F-Distribution.html" target="_top">Weisstein,
Eric W. "F-Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
</td>
</tr>
</tbody>
@@ -433,7 +437,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="extreme_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="gamma_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="extreme_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="gamma_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Gamma (and Erlang) Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="f_dist.html" title="F Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="f_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="hypergeometric_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="f_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="hypergeometric_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist"></a><a class="link" href="gamma_dist.html" title="Gamma (and Erlang) Distribution"> Gamma
(and Erlang) Distribution</a>
@@ -65,7 +65,7 @@
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../../doc/html/images/note.png"></td>
<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">
@@ -137,7 +137,7 @@
than a dedicated Erlang Distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions"></a><h5>
<a name="id901333"></a>
<a name="id869693"></a>
<a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.member_functions">Member
Functions</a>
</h5>
@@ -162,7 +162,7 @@
Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors"></a><h5>
<a name="id901478"></a>
<a name="id869873"></a>
<a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -182,7 +182,7 @@
The domain of the random variable is [0,+&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy"></a><h5>
<a name="id901575"></a>
<a name="id870021"></a>
<a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -194,7 +194,7 @@
refer to the accuracy data for those functions for more information.
</p>
<a name="math_toolkit.dist.dist_ref.dists.gamma_dist.implementation"></a><h5>
<a name="id901614"></a>
<a name="id870083"></a>
<a class="link" href="gamma_dist.html#math_toolkit.dist.dist_ref.dists.gamma_dist.implementation">Implementation</a>
</h5>
<p>
@@ -210,152 +210,152 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = <a class="link" href="../../../special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">gamma_p_derivative</a>(k,
x / &#952;) / &#952;
</p>
<p>
Using the relation: pdf = <a class="link" href="../../../special/sf_gamma/gamma_derivatives.html" title="Derivative of the Incomplete Gamma Function">gamma_p_derivative</a>(k,
x / &#952;) / &#952;
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: p = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>(k,
x / &#952;)
</p>
<p>
Using the relation: p = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>(k,
x / &#952;)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>(k,
x / &#952;)
</p>
<p>
Using the relation: q = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>(k,
x / &#952;)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: x = &#952;* <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>(k,
p)
</p>
<p>
Using the relation: x = &#952;* <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inv</a>(k,
p)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: x = &#952;* <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>(k,
p)
</p>
<p>
Using the relation: x = &#952;* <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inv</a>(k,
p)
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
k&#952;
</p>
<p>
k&#952;
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
k&#952;<sup>2</sup>
</p>
<p>
k&#952;<sup>2</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
(k-1)&#952; for <span class="emphasis"><em>k&gt;1</em></span> otherwise a <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>
</p>
<p>
(k-1)&#952; for <span class="emphasis"><em>k&gt;1</em></span> otherwise a <a class="link" href="../../../main_overview/error_handling.html#domain_error">domain_error</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
2 / sqrt(k)
</p>
<p>
2 / sqrt(k)
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
3 + 6 / k
</p>
<p>
3 + 6 / k
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
6 / k
</p>
<p>
6 / k
</p>
</td>
</tr>
</tbody>
@@ -373,7 +373,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="f_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="hypergeometric_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Hypergeometric Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="gamma_dist.html" title="Gamma (and Erlang) Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="gamma_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="laplace_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="gamma_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="laplace_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist"></a><a class="link" href="hypergeometric_dist.html" title="Hypergeometric Distribution">
Hypergeometric Distribution</a>
@@ -75,7 +75,7 @@
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../../doc/html/images/note.png"></td>
<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>
@@ -102,7 +102,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/hypergeometric_pdf_2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions"></a><h5>
<a name="id902470"></a>
<a name="id871115"></a>
<a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.member_functions">Member
Functions</a>
</h5>
@@ -131,7 +131,7 @@
from the population <span class="emphasis"><em>N</em></span>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors"></a><h5>
<a name="id902649"></a>
<a name="id871335"></a>
<a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -155,7 +155,7 @@
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/html/images/caution.png"></td>
<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">
@@ -185,7 +185,7 @@
</td></tr>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy"></a><h5>
<a name="id905497"></a>
<a name="id871570"></a>
<a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -211,7 +211,7 @@
meaningless for N &gt;= 10<sup>15</sup>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing"></a><h5>
<a name="id905731"></a>
<a name="id871853"></a>
<a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.testing">Testing</a>
</h5>
<p>
@@ -223,7 +223,7 @@
this implementation and NTL::RR.
</p>
<a name="math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation"></a><h5>
<a name="id905755"></a>
<a name="id871911"></a>
<a class="link" href="hypergeometric_dist.html#math_toolkit.dist.dist_ref.dists.hypergeometric_dist.implementation">Implementation</a>
</h5>
<p>
@@ -338,7 +338,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="gamma_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="laplace_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="gamma_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="laplace_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Laplace Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="hypergeometric_dist.html" title="Hypergeometric Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="hypergeometric_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="logistic_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="hypergeometric_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="logistic_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist"></a><a class="link" href="laplace_dist.html" title="Laplace Distribution"> Laplace
Distribution</a>
@@ -81,7 +81,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/laplace_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions"></a><h5>
<a name="id906483"></a>
<a name="id872764"></a>
<a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.member_functions">Member
Functions</a>
</h5>
@@ -113,7 +113,7 @@
Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors"></a><h5>
<a name="id906645"></a>
<a name="id873011"></a>
<a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -133,7 +133,7 @@
The domain of the random variable is [-&#8734;,+&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy"></a><h5>
<a name="id906742"></a>
<a name="id873160"></a>
<a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -141,7 +141,7 @@
log and exp functions and as such should have very small errors.
</p>
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.implementation"></a><h5>
<a name="id906761"></a>
<a name="id873188"></a>
<a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.implementation">Implementation</a>
</h5>
<p>
@@ -157,193 +157,195 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = e<sup>-abs(x-&#956;) / &#963;</sup> / (2 * &#963;)
</p>
<p>
Using the relation: pdf = e<sup>-abs(x-&#956;) / &#963;</sup> / (2 * &#963;)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relations:
</p>
<p>
x &lt; &#956; : p = e<sup>(x-&#956;)/&#963; </sup> / &#963;
</p>
<p>
x &gt;= &#956; : p = 1 - e<sup>(&#956;-x)/&#963; </sup> / &#963;
<p>
Using the relations:
</p>
<p>
x &lt; &#956; : p = e<sup>(x-&#956;)/&#963; </sup> / &#963;
</p>
<p>
x &gt;= &#956; : p = 1 - e<sup>(&#956;-x)/&#963; </sup> / &#963;
</p>
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
-x &lt; &#956; : q = e<sup>(-x-&#956;)/&#963; </sup> / &#963;
</p>
<p>
-x &gt;= &#956; : q = 1 - e<sup>(&#956;+x)/&#963; </sup> / &#963;
<p>
Using the relation:
</p>
<p>
-x &lt; &#956; : q = e<sup>(-x-&#956;)/&#963; </sup> / &#963;
</p>
<p>
-x &gt;= &#956; : q = 1 - e<sup>(&#956;+x)/&#963; </sup> / &#963;
</p>
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relations:
</p>
<p>
p &lt; 0.5 : x = &#956; + &#963; * log(2*p)
</p>
<p>
p &gt;= 0.5 : x = &#956; - &#963; * log(2-2*p)
</p>
<p>
Using the relations:
</p>
<p>
p &lt; 0.5 : x = &#956; + &#963; * log(2*p)
</p>
<p>
p &gt;= 0.5 : x = &#956; - &#963; * log(2-2*p)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
q &gt; 0.5: x = &#956; + &#963;*log(2-2*q)
</p>
<p>
q &lt;=0.5: x = &#956; - &#963;*log( 2*q )
</p>
<p>
Using the relation:
</p>
<p>
q &gt; 0.5: x = &#956; + &#963;*log(2-2*q)
</p>
<p>
q &lt;=0.5: x = &#956; - &#963;*log( 2*q )
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
&#956;
</p>
<p>
&#956;
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
2 * &#963;<sup>2</sup>
</p>
<p>
2 * &#963;<sup>2</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
&#956;
</p>
<p>
&#956;
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
0
</p>
<p>
0
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
6
</p>
<p>
6
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
3
</p>
<p>
3
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.laplace_dist.references"></a><h5>
<a name="id907069"></a>
<a name="id873534"></a>
<a class="link" href="laplace_dist.html#math_toolkit.dist.dist_ref.dists.laplace_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li>
<a href="http://mathworld.wolfram.com/LaplaceDistribution.html" target="_top">Weisstein,
Eric W. "Laplace Distribution."</a> From MathWorld--A
Wolfram Web Resource.
</li>
<li><a href="http://en.wikipedia.org/wiki/Laplace_distribution" target="_top">Laplace
Distribution</a></li>
<li>
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions,
1972, p. 930.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a href="http://mathworld.wolfram.com/LaplaceDistribution.html" target="_top">Weisstein,
Eric W. "Laplace Distribution."</a> From MathWorld--A
Wolfram Web Resource.
</li>
<li class="listitem">
<a href="http://en.wikipedia.org/wiki/Laplace_distribution" target="_top">Laplace
Distribution</a>
</li>
<li class="listitem">
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions,
1972, p. 930.
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -358,7 +360,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="hypergeometric_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="logistic_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
</body>
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View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Logistic Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="laplace_dist.html" title="Laplace Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="laplace_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lognormal_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="laplace_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="lognormal_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist"></a><a class="link" href="logistic_dist.html" title="Logistic Distribution">
Logistic Distribution</a>
@@ -72,7 +72,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/logistic_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions"></a><h5>
<a name="id907548"></a>
<a name="id874399"></a>
<a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.member_functions">Member
Functions</a>
</h5>
@@ -98,7 +98,7 @@
Returns the scale of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors"></a><h5>
<a name="id907778"></a>
<a name="id874602"></a>
<a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -128,7 +128,7 @@ as special cases if RealType
and +<a class="link" href="../../../main_overview/error_handling.html#overflow_error">overflow_error</a> respectively.
</p>
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy"></a><h5>
<a name="id907928"></a>
<a name="id874826"></a>
<a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -140,7 +140,7 @@ as special cases if RealType
error</em></span> can be guarenteed.
</p>
<a name="math_toolkit.dist.dist_ref.dists.logistic_dist.implementation"></a><h5>
<a name="id907983"></a>
<a name="id874902"></a>
<a class="link" href="logistic_dist.html#math_toolkit.dist.dist_ref.dists.logistic_dist.implementation">Implementation</a>
</h5>
<div class="informaltable"><table class="table">
@@ -150,135 +150,135 @@ as special cases if RealType
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = e<sup>-(x-u)/s</sup> / (s*(1+e<sup>-(x-u)/s</sup>)<sup>2</sup>)
</p>
<p>
Using the relation: pdf = e<sup>-(x-u)/s</sup> / (s*(1+e<sup>-(x-u)/s</sup>)<sup>2</sup>)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: p = 1/(1+e<sup>-(x-u)/s</sup>)
</p>
<p>
Using the relation: p = 1/(1+e<sup>-(x-u)/s</sup>)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = 1/(1+e<sup>(x-u)/s</sup>)
</p>
<p>
Using the relation: q = 1/(1+e<sup>(x-u)/s</sup>)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: x = u - s*log(1/p-1)
</p>
<p>
Using the relation: x = u - s*log(1/p-1)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: x = u + s*log(p/1-p)
</p>
<p>
Using the relation: x = u + s*log(p/1-p)
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
u
</p>
<p>
u
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
The same as the mean.
</p>
<p>
The same as the mean.
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
0
</p>
<p>
0
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
6/5
</p>
<p>
6/5
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
(&#960;*s)<sup>2</sup> / 3
</p>
<p>
(&#960;*s)<sup>2</sup> / 3
</p>
</td>
</tr>
</tbody>
@@ -296,7 +296,7 @@ as special cases if RealType
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="laplace_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="lognormal_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Log Normal Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="logistic_dist.html" title="Logistic Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="logistic_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="negative_binomial_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist"></a><a class="link" href="lognormal_dist.html" title="Log Normal Distribution">
Log Normal Distribution</a>
@@ -88,7 +88,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/lognormal_pdf2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions"></a><h5>
<a name="id908718"></a>
<a name="id875688"></a>
<a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.member_functions">Member
Functions</a>
</h5>
@@ -121,7 +121,7 @@
Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors"></a><h5>
<a name="id908878"></a>
<a name="id875972"></a>
<a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -141,7 +141,7 @@
The domain of the random variable is [0,+&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy"></a><h5>
<a name="id908978"></a>
<a name="id876119"></a>
<a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -150,7 +150,7 @@
function</a>, and as such should have very low error rates.
</p>
<a name="math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation"></a><h5>
<a name="id909005"></a>
<a name="id876156"></a>
<a class="link" href="lognormal_dist.html#math_toolkit.dist.dist_ref.dists.lognormal_dist.implementation">Implementation</a>
</h5>
<p>
@@ -166,151 +166,151 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = e<sup>-(ln(x) - m)<sup>2 </sup> / 2s<sup>2 </sup> </sup> / (x * s * sqrt(2pi))
</p>
<p>
Using the relation: pdf = e<sup>-(ln(x) - m)<sup>2 </sup> / 2s<sup>2 </sup> </sup> / (x * s * sqrt(2pi))
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: p = cdf(normal_distribtion&lt;RealType&gt;(m,
s), log(x))
</p>
<p>
Using the relation: p = cdf(normal_distribtion&lt;RealType&gt;(m,
s), log(x))
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = cdf(complement(normal_distribtion&lt;RealType&gt;(m,
s), log(x)))
</p>
<p>
Using the relation: q = cdf(complement(normal_distribtion&lt;RealType&gt;(m,
s), log(x)))
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: x = exp(quantile(normal_distribtion&lt;RealType&gt;(m,
s), p))
</p>
<p>
Using the relation: x = exp(quantile(normal_distribtion&lt;RealType&gt;(m,
s), p))
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: x = exp(quantile(complement(normal_distribtion&lt;RealType&gt;(m,
s), q)))
</p>
<p>
Using the relation: x = exp(quantile(complement(normal_distribtion&lt;RealType&gt;(m,
s), q)))
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
e<sup>m + s<sup>2 </sup> / 2 </sup>
</p>
<p>
e<sup>m + s<sup>2 </sup> / 2 </sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
(e<sup>s<sup>2</sup> </sup> - 1) * e<sup>2m + s<sup>2 </sup> </sup>
</p>
<p>
(e<sup>s<sup>2</sup> </sup> - 1) * e<sup>2m + s<sup>2 </sup> </sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
e<sup>m + s<sup>2 </sup> </sup>
</p>
<p>
e<sup>m + s<sup>2 </sup> </sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
sqrt(e<sup>s<sup>2</sup> </sup> - 1) * (2 + e<sup>s<sup>2</sup> </sup>)
</p>
<p>
sqrt(e<sup>s<sup>2</sup> </sup> - 1) * (2 + e<sup>s<sup>2</sup> </sup>)
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
e<sup>4s<sup>2</sup> </sup> + 2e<sup>3s<sup>2</sup> </sup> + 3e<sup>2s<sup>2</sup> </sup> - 3
</p>
<p>
e<sup>4s<sup>2</sup> </sup> + 2e<sup>3s<sup>2</sup> </sup> + 3e<sup>2s<sup>2</sup> </sup> - 3
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
e<sup>4s<sup>2</sup> </sup> + 2e<sup>3s<sup>2</sup> </sup> + 3e<sup>2s<sup>2</sup> </sup> - 6
</p>
<p>
e<sup>4s<sup>2</sup> </sup> + 2e<sup>3s<sup>2</sup> </sup> + 3e<sup>2s<sup>2</sup> </sup> - 6
</p>
</td>
</tr>
</tbody>
@@ -328,7 +328,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="logistic_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="negative_binomial_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Noncentral Beta Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="negative_binomial_dist.html" title="Negative Binomial Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
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<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist"></a><a class="link" href="nc_beta_dist.html" title="Noncentral Beta Distribution"> Noncentral
Beta Distribution</a>
@@ -96,7 +96,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
<span class="inlinemediaobject"><img src="../../../../../graphs/nc_beta_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions"></a><h5>
<a name="id913536"></a>
<a name="id881401"></a>
<a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.member_functions">Member
Functions</a>
</h5>
@@ -128,7 +128,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
was constructed.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.non_member_accessors"></a><h5>
<a name="id913722"></a>
<a name="id881671"></a>
<a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -152,7 +152,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
The domain of the random variable is [0, 1].
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy"></a><h5>
<a name="id913823"></a>
<a name="id881822"></a>
<a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -168,7 +168,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
zero error</a>.
</p>
<div class="table">
<a name="id913858"></a><p class="title"><b>Table&#160;13.&#160;Errors In CDF of the Noncentral Beta</b></p>
<a name="id881877"></a><p class="title"><b>Table&#160;13.&#160;Errors In CDF of the Noncentral Beta</b></p>
<div class="table-contents"><table class="table" summary="Errors In CDF of the Noncentral Beta">
<colgroup>
<col>
@@ -178,114 +178,114 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
</colgroup>
<thead><tr>
<th>
<p>
Significand Size
</p>
</th>
<p>
Significand Size
</p>
</th>
<th>
<p>
Platform and Compiler
</p>
</th>
<p>
Platform and Compiler
</p>
</th>
<th>
<p>
&#945;, &#946;,&#955; &lt; 200
</p>
</th>
<p>
&#945;, &#946;,&#955; &lt; 200
</p>
</th>
<th>
<p>
&#945;,&#946;,&#955; &gt; 200
</p>
</th>
<p>
&#945;,&#946;,&#955; &gt; 200
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
53
</p>
</td>
<p>
53
</p>
</td>
<td>
<p>
Win32, Visual C++ 8
</p>
</td>
<p>
Win32, Visual C++ 8
</p>
</td>
<td>
<p>
Peak=620 Mean=22
</p>
</td>
<p>
Peak=620 Mean=22
</p>
</td>
<td>
<p>
Peak=8670 Mean=1040
</p>
</td>
<p>
Peak=8670 Mean=1040
</p>
</td>
</tr>
<tr>
<td>
<p>
64
</p>
</td>
<p>
64
</p>
</td>
<td>
<p>
RedHat Linux IA32, gcc-4.1.1
</p>
</td>
<p>
RedHat Linux IA32, gcc-4.1.1
</p>
</td>
<td>
<p>
Peak=825 Mean=50
</p>
</td>
<p>
Peak=825 Mean=50
</p>
</td>
<td>
<p>
Peak=2.5x10<sup>4</sup> Mean=4000
</p>
</td>
<p>
Peak=2.5x10<sup>4</sup> Mean=4000
</p>
</td>
</tr>
<tr>
<td>
<p>
64
</p>
</td>
<p>
64
</p>
</td>
<td>
<p>
Redhat Linux IA64, gcc-3.4.4
</p>
</td>
<p>
Redhat Linux IA64, gcc-3.4.4
</p>
</td>
<td>
<p>
Peak=825 Mean=30
</p>
</td>
<p>
Peak=825 Mean=30
</p>
</td>
<td>
<p>
Peak=1.7x10<sup>4</sup> Mean=2500
</p>
</td>
<p>
Peak=1.7x10<sup>4</sup> Mean=2500
</p>
</td>
</tr>
<tr>
<td>
<p>
113
</p>
</td>
<p>
113
</p>
</td>
<td>
<p>
HPUX IA64, aCC A.06.06
</p>
</td>
<p>
HPUX IA64, aCC A.06.06
</p>
</td>
<td>
<p>
Peak=420 Mean=50
</p>
</td>
<p>
Peak=420 Mean=50
</p>
</td>
<td>
<p>
Peak=9200 Mean=1200
</p>
</td>
<p>
Peak=9200 Mean=1200
</p>
</td>
</tr>
</tbody>
</table></div>
@@ -295,7 +295,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
functions are broadly similar.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests"></a><h5>
<a name="id914041"></a>
<a name="id882084"></a>
<a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.tests">Tests</a>
</h5>
<p>
@@ -307,7 +307,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
tests.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation"></a><h5>
<a name="id914065"></a>
<a name="id882123"></a>
<a class="link" href="nc_beta_dist.html#math_toolkit.dist.dist_ref.dists.nc_beta_dist.implementation">Implementation</a>
</h5>
<p>
@@ -408,7 +408,7 @@ is a central &#967;<sup>2</sup> random variable with <span class="emphasis"><em>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="negative_binomial_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_chi_squared_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Noncentral Chi-Squared Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_beta_dist.html" title="Noncentral Beta Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="nc_beta_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_f_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist"></a><a class="link" href="nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">
Noncentral Chi-Squared Distribution</a>
@@ -110,7 +110,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/nccs_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.member_functions"></a><h5>
<a name="id915805"></a>
<a name="id883388"></a>
<a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.member_functions">Member
Functions</a>
</h5>
@@ -183,7 +183,7 @@
<span class="special">==</span> <span class="identifier">q</span></code>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.non_member_accessors"></a><h5>
<a name="id916706"></a>
<a name="id884476"></a>
<a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -203,7 +203,7 @@
The domain of the random variable is [0, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples"></a><h5>
<a name="id916806"></a>
<a name="id884624"></a>
<a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.examples">Examples</a>
</h5>
<p>
@@ -211,7 +211,7 @@
example</a> for the noncentral chi-squared distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy"></a><h5>
<a name="id916834"></a>
<a name="id884659"></a>
<a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -223,7 +223,7 @@
zero error</a>.
</p>
<div class="table">
<a name="id916864"></a><p class="title"><b>Table&#160;14.&#160;Errors In CDF of the Noncentral Chi-Squared</b></p>
<a name="id884703"></a><p class="title"><b>Table&#160;14.&#160;Errors In CDF of the Noncentral Chi-Squared</b></p>
<div class="table-contents"><table class="table" summary="Errors In CDF of the Noncentral Chi-Squared">
<colgroup>
<col>
@@ -233,120 +233,120 @@
</colgroup>
<thead><tr>
<th>
<p>
Significand Size
</p>
</th>
<p>
Significand Size
</p>
</th>
<th>
<p>
Platform and Compiler
</p>
</th>
<p>
Platform and Compiler
</p>
</th>
<th>
<p>
&#957;,&#955; &lt; 200
</p>
</th>
<p>
&#957;,&#955; &lt; 200
</p>
</th>
<th>
<p>
&#957;,&#955; &gt; 200
</p>
</th>
<p>
&#957;,&#955; &gt; 200
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
53
</p>
</td>
<p>
53
</p>
</td>
<td>
<p>
Win32, Visual C++ 8
</p>
</td>
<p>
Win32, Visual C++ 8
</p>
</td>
<td>
<p>
Peak=50 Mean=9.9
</p>
<p>
R Peak=685 Mean=109
</p>
</td>
<p>
Peak=50 Mean=9.9
</p>
<p>
R Peak=685 Mean=109
</p>
</td>
<td>
<p>
Peak=9780 Mean=718
</p>
<p>
R Peak=3x10<sup>8</sup> Mean=2x10<sup>7</sup>
</p>
</td>
<p>
Peak=9780 Mean=718
</p>
<p>
R Peak=3x10<sup>8</sup> Mean=2x10<sup>7</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
64
</p>
</td>
<p>
64
</p>
</td>
<td>
<p>
RedHat Linux IA32, gcc-4.1.1
</p>
</td>
<p>
RedHat Linux IA32, gcc-4.1.1
</p>
</td>
<td>
<p>
Peak=270 Mean=27
</p>
</td>
<p>
Peak=270 Mean=27
</p>
</td>
<td>
<p>
Peak=7900 Mean=900
</p>
</td>
<p>
Peak=7900 Mean=900
</p>
</td>
</tr>
<tr>
<td>
<p>
64
</p>
</td>
<p>
64
</p>
</td>
<td>
<p>
Redhat Linux IA64, gcc-3.4.4
</p>
</td>
<p>
Redhat Linux IA64, gcc-3.4.4
</p>
</td>
<td>
<p>
Peak=107 Mean=17
</p>
</td>
<p>
Peak=107 Mean=17
</p>
</td>
<td>
<p>
Peak=5000 Mean=630
</p>
</td>
<p>
Peak=5000 Mean=630
</p>
</td>
</tr>
<tr>
<td>
<p>
113
</p>
</td>
<p>
113
</p>
</td>
<td>
<p>
HPUX IA64, aCC A.06.06
</p>
</td>
<p>
HPUX IA64, aCC A.06.06
</p>
</td>
<td>
<p>
Peak=270 Mean=20
</p>
</td>
<p>
Peak=270 Mean=20
</p>
</td>
<td>
<p>
Peak=4600 Mean=560
</p>
</td>
<p>
Peak=4600 Mean=560
</p>
</td>
</tr>
</tbody>
</table></div>
@@ -359,7 +359,7 @@
produce an accuracy greater than the square root of the machine epsilon.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests"></a><h5>
<a name="id917062"></a>
<a name="id884931"></a>
<a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.tests">Tests</a>
</h5>
<p>
@@ -373,7 +373,7 @@
to at least 50 decimal digits - and is the used for our accuracy tests.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation"></a><h5>
<a name="id917081"></a>
<a name="id884958"></a>
<a class="link" href="nc_chi_squared_dist.html#math_toolkit.dist.dist_ref.dists.nc_chi_squared_dist.implementation">Implementation</a>
</h5>
<p>
@@ -510,7 +510,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="nc_beta_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_f_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Noncentral F Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_chi_squared_dist.html" title="Noncentral Chi-Squared Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="nc_chi_squared_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_t_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist"></a><a class="link" href="nc_f_dist.html" title="Noncentral F Distribution"> Noncentral
F Distribution</a>
@@ -95,7 +95,7 @@ random variable with <span class="emphasis"><em>v1</em></span>
<span class="inlinemediaobject"><img src="../../../../../graphs/nc_f_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions"></a><h5>
<a name="id920324"></a>
<a name="id885988"></a>
<a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.member_functions">Member
Functions</a>
</h5>
@@ -127,7 +127,7 @@ random variable with <span class="emphasis"><em>v1</em></span>
which this object was constructed.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.non_member_accessors"></a><h5>
<a name="id920513"></a>
<a name="id886258"></a>
<a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -147,7 +147,7 @@ random variable with <span class="emphasis"><em>v1</em></span>
The domain of the random variable is [0, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy"></a><h5>
<a name="id920612"></a>
<a name="id886407"></a>
<a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -155,7 +155,7 @@ random variable with <span class="emphasis"><em>v1</em></span>
Beta Distribution</a>: refer to that distribution for accuracy data.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.tests"></a><h5>
<a name="id920636"></a>
<a name="id886443"></a>
<a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.tests">Tests</a>
</h5>
<p>
@@ -164,7 +164,7 @@ random variable with <span class="emphasis"><em>v1</em></span>
Math library statistical package</a> and its pbeta and dbeta functions.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation"></a><h5>
<a name="id920660"></a>
<a name="id886478"></a>
<a class="link" href="nc_f_dist.html#math_toolkit.dist.dist_ref.dists.nc_f_dist.implementation">Implementation</a>
</h5>
<p>
@@ -182,216 +182,217 @@ is the non-centrality parameter, <span class="emphasis"><em>x</em></span> is the
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Implemented in terms of the non-central beta PDF using the relation:
</p>
<p>
f(x;v1,v2;&#955;) = (v1/v2) / ((1+y)*(1+y)) * g(y/(1+y);v1/2,v2/2;&#955;)
</p>
<p>
where g(x; a, b; &#955;) is the non central beta PDF, and:
</p>
<p>
y = x * v1 / v2
</p>
<p>
Implemented in terms of the non-central beta PDF using the
relation:
</p>
<p>
f(x;v1,v2;&#955;) = (v1/v2) / ((1+y)*(1+y)) * g(y/(1+y);v1/2,v2/2;&#955;)
</p>
<p>
where g(x; a, b; &#955;) is the non central beta PDF, and:
</p>
<p>
y = x * v1 / v2
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
p = B<sub>y</sub>(v1/2, v2/2; &#955;)
</p>
<p>
where B<sub>x</sub>(a, b; &#955;) is the noncentral beta distribution CDF and
</p>
<p>
y = x * v1 / v2
</p>
<p>
</p>
<p>
Using the relation:
</p>
<p>
p = B<sub>y</sub>(v1/2, v2/2; &#955;)
</p>
<p>
where B<sub>x</sub>(a, b; &#955;) is the noncentral beta distribution CDF and
</p>
<p>
y = x * v1 / v2
</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
q = 1 - B<sub>y</sub>(v1/2, v2/2; &#955;)
</p>
<p>
where 1 - B<sub>x</sub>(a, b; &#955;) is the complement of the noncentral beta
distribution CDF and
</p>
<p>
y = x * v1 / v2
</p>
<p>
</p>
<p>
Using the relation:
</p>
<p>
q = 1 - B<sub>y</sub>(v1/2, v2/2; &#955;)
</p>
<p>
where 1 - B<sub>x</sub>(a, b; &#955;) is the complement of the noncentral beta
distribution CDF and
</p>
<p>
y = x * v1 / v2
</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
x = (bx / (1-bx)) * (v1 / v2)
</p>
<p>
where
</p>
<p>
bx = Q<sub>p</sub><sup>-1</sup>(v1/2, v2/2; &#955;)
</p>
<p>
and
</p>
<p>
Q<sub>p</sub><sup>-1</sup>(v1/2, v2/2; &#955;)
</p>
<p>
is the noncentral beta quantile.
</p>
<p>
</p>
<p>
Using the relation:
</p>
<p>
x = (bx / (1-bx)) * (v1 / v2)
</p>
<p>
where
</p>
<p>
bx = Q<sub>p</sub><sup>-1</sup>(v1/2, v2/2; &#955;)
</p>
<p>
and
</p>
<p>
Q<sub>p</sub><sup>-1</sup>(v1/2, v2/2; &#955;)
</p>
<p>
is the noncentral beta quantile.
</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
from the complement
</p>
<p>
quantile
</p>
<p>
from the complement
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
x = (bx / (1-bx)) * (v1 / v2)
</p>
<p>
where
</p>
<p>
bx = QC<sub>q</sub><sup>-1</sup>(v1/2, v2/2; &#955;)
</p>
<p>
and
</p>
<p>
QC<sub>q</sub><sup>-1</sup>(v1/2, v2/2; &#955;)
</p>
<p>
is the noncentral beta quantile from the complement.
</p>
<p>
Using the relation:
</p>
<p>
x = (bx / (1-bx)) * (v1 / v2)
</p>
<p>
where
</p>
<p>
bx = QC<sub>q</sub><sup>-1</sup>(v1/2, v2/2; &#955;)
</p>
<p>
and
</p>
<p>
QC<sub>q</sub><sup>-1</sup>(v1/2, v2/2; &#955;)
</p>
<p>
is the noncentral beta quantile from the complement.
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
v2 * (v1 + l) / (v1 * (v2 - 2))
</p>
<p>
v2 * (v1 + l) / (v1 * (v2 - 2))
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
By numeric maximalisation of the PDF.
</p>
<p>
By numeric maximalisation of the PDF.
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
Refer to, <a href="http://mathworld.wolfram.com/NoncentralF-Distribution.html" target="_top">Weisstein,
Eric W. "Noncentral F-Distribution." From MathWorld--A
Wolfram Web Resource.</a>
</p>
<p>
Refer to, <a href="http://mathworld.wolfram.com/NoncentralF-Distribution.html" target="_top">Weisstein,
Eric W. "Noncentral F-Distribution." From MathWorld--A
Wolfram Web Resource.</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
Refer to, <a href="http://mathworld.wolfram.com/NoncentralF-Distribution.html" target="_top">Weisstein,
Eric W. "Noncentral F-Distribution." From MathWorld--A
Wolfram Web Resource.</a>, and to the <a href="http://reference.wolfram.com/mathematica/ref/NoncentralFRatioDistribution.html" target="_top">Mathematica
documentation</a>
</p>
<p>
Refer to, <a href="http://mathworld.wolfram.com/NoncentralF-Distribution.html" target="_top">Weisstein,
Eric W. "Noncentral F-Distribution." From MathWorld--A
Wolfram Web Resource.</a>, and to the <a href="http://reference.wolfram.com/mathematica/ref/NoncentralFRatioDistribution.html" target="_top">Mathematica
documentation</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis and kurtosis excess
</p>
<p>
kurtosis and kurtosis excess
</p>
</td>
<td>
<p>
Refer to, <a href="http://mathworld.wolfram.com/NoncentralF-Distribution.html" target="_top">Weisstein,
Eric W. "Noncentral F-Distribution." From MathWorld--A
Wolfram Web Resource.</a>, and to the <a href="http://reference.wolfram.com/mathematica/ref/NoncentralFRatioDistribution.html" target="_top">Mathematica
documentation</a>
</p>
<p>
Refer to, <a href="http://mathworld.wolfram.com/NoncentralF-Distribution.html" target="_top">Weisstein,
Eric W. "Noncentral F-Distribution." From MathWorld--A
Wolfram Web Resource.</a>, and to the <a href="http://reference.wolfram.com/mathematica/ref/NoncentralFRatioDistribution.html" target="_top">Mathematica
documentation</a>
</p>
</td>
</tr>
</tbody>
@@ -417,7 +418,7 @@ is the non-centrality parameter, <span class="emphasis"><em>x</em></span> is the
</tr></table>
<hr>
<div class="spirit-nav">
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View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Noncentral T Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_f_dist.html" title="Noncentral F Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="nc_f_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="normal_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="nc_f_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="normal_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist"></a><a class="link" href="nc_t_dist.html" title="Noncentral T Distribution"> Noncentral
T Distribution</a>
@@ -85,7 +85,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/nc_t_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions"></a><h5>
<a name="id921539"></a>
<a name="id887489"></a>
<a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.member_functions">Member
Functions</a>
</h5>
@@ -111,7 +111,7 @@
which this object was constructed.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.non_member_accessors"></a><h5>
<a name="id921678"></a>
<a name="id887703"></a>
<a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -131,7 +131,7 @@
The domain of the random variable is [-&#8734;, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy"></a><h5>
<a name="id921778"></a>
<a name="id887852"></a>
<a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -141,7 +141,7 @@
one shown will have <a class="link" href="../../../backgrounders/relative_error.html#zero_error">effectively zero error</a>.
</p>
<div class="table">
<a name="id921800"></a><p class="title"><b>Table&#160;15.&#160;Errors In CDF of the Noncentral T Distribution</b></p>
<a name="id887888"></a><p class="title"><b>Table&#160;15.&#160;Errors In CDF of the Noncentral T Distribution</b></p>
<div class="table-contents"><table class="table" summary="Errors In CDF of the Noncentral T Distribution">
<colgroup>
<col>
@@ -150,96 +150,96 @@
</colgroup>
<thead><tr>
<th>
<p>
Significand Size
</p>
</th>
<p>
Significand Size
</p>
</th>
<th>
<p>
Platform and Compiler
</p>
</th>
<p>
Platform and Compiler
</p>
</th>
<th>
<p>
&#957;,&#948; &lt; 600
</p>
</th>
<p>
&#957;,&#948; &lt; 600
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
53
</p>
</td>
<p>
53
</p>
</td>
<td>
<p>
Win32, Visual C++ 8
</p>
</td>
<p>
Win32, Visual C++ 8
</p>
</td>
<td>
<p>
Peak=120 Mean=26
</p>
</td>
<p>
Peak=120 Mean=26
</p>
</td>
</tr>
<tr>
<td>
<p>
64
</p>
</td>
<p>
64
</p>
</td>
<td>
<p>
RedHat Linux IA32, gcc-4.1.1
</p>
</td>
<p>
RedHat Linux IA32, gcc-4.1.1
</p>
</td>
<td>
<p>
Peak=121 Mean=26
</p>
</td>
<p>
Peak=121 Mean=26
</p>
</td>
</tr>
<tr>
<td>
<p>
64
</p>
</td>
<p>
64
</p>
</td>
<td>
<p>
Redhat Linux IA64, gcc-3.4.4
</p>
</td>
<p>
Redhat Linux IA64, gcc-3.4.4
</p>
</td>
<td>
<p>
Peak=122 Mean=25
</p>
</td>
<p>
Peak=122 Mean=25
</p>
</td>
</tr>
<tr>
<td>
<p>
113
</p>
</td>
<p>
113
</p>
</td>
<td>
<p>
HPUX IA64, aCC A.06.06
</p>
</td>
<p>
HPUX IA64, aCC A.06.06
</p>
</td>
<td>
<p>
Peak=115 Mean=24
</p>
</td>
<p>
Peak=115 Mean=24
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/html/images/caution.png"></td>
<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>
@@ -255,7 +255,7 @@
epsilon.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.tests"></a><h5>
<a name="id921959"></a>
<a name="id888050"></a>
<a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.tests">Tests</a>
</h5>
<p>
@@ -270,7 +270,7 @@
least 50 decimal places.
</p>
<a name="math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation"></a><h5>
<a name="id921978"></a>
<a name="id888100"></a>
<a class="link" href="nc_t_dist.html#math_toolkit.dist.dist_ref.dists.nc_t_dist.implementation">Implementation</a>
</h5>
<p>
@@ -361,7 +361,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="nc_f_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="normal_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Negative Binomial Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
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<link rel="up" href="../dists.html" title="Distributions">
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@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="lognormal_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_beta_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist"></a><a class="link" href="negative_binomial_dist.html" title="Negative Binomial Distribution">
Negative Binomial Distribution</a>
@@ -92,7 +92,7 @@
</p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../../doc/html/images/note.png"></td>
<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>
@@ -123,7 +123,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/negative_binomial_pdf_2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions"></a><h5>
<a name="id910137"></a>
<a name="id877479"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.related_distributions">Related
Distributions</a>
</h5>
@@ -164,7 +164,7 @@
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/html/images/caution.png"></td>
<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">
@@ -200,12 +200,12 @@
<p>
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.member_functions"></a><h5>
<a name="id910248"></a>
<a name="id877664"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.member_functions">Member
Functions</a>
</h5>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.construct"></a><h6>
<a name="id910261"></a>
<a name="id877687"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.construct">Construct</a>
</h6>
<pre class="programlisting"><span class="identifier">negative_binomial_distribution</span><span class="special">(</span><span class="identifier">RealType</span> <span class="identifier">r</span><span class="special">,</span> <span class="identifier">RealType</span> <span class="identifier">p</span><span class="special">);</span>
@@ -221,7 +221,7 @@
<span class="special">&lt;=</span> <span class="number">1</span></code>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors"></a><h6>
<a name="id910370"></a>
<a name="id877824"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accessors">Accessors</a>
</h6>
<pre class="programlisting"><span class="identifier">RealType</span> <span class="identifier">success_fraction</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span> <span class="comment">// successes / trials (0 &lt;= p &lt;= 1)
@@ -237,7 +237,7 @@
was constructed.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.lower_bound_on_parameter_p"></a><h6>
<a name="id910455"></a>
<a name="id877937"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.lower_bound_on_parameter_p">Lower
Bound on Parameter p</a>
</h6>
@@ -255,18 +255,18 @@
<dl>
<dt><span class="term">failures</span></dt>
<dd><p>
The total number of failures before the r th success.
</p></dd>
The total number of failures before the r th success.
</p></dd>
<dt><span class="term">successes</span></dt>
<dd><p>
The number of successes required.
</p></dd>
The number of successes required.
</p></dd>
<dt><span class="term">alpha</span></dt>
<dd><p>
The largest acceptable probability that the true value of the success
fraction is <span class="bold"><strong>less than</strong></span> the value
returned.
</p></dd>
The largest acceptable probability that the true value of the success
fraction is <span class="bold"><strong>less than</strong></span> the value
returned.
</p></dd>
</dl>
</div>
<p>
@@ -298,7 +298,7 @@
vol. 48, no3, 605-621</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.upper_bound_on_parameter_p"></a><h6>
<a name="id910719"></a>
<a name="id878264"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.upper_bound_on_parameter_p">Upper
Bound on Parameter p</a>
</h6>
@@ -316,18 +316,18 @@
<dl>
<dt><span class="term">trials</span></dt>
<dd><p>
The total number of trials conducted.
</p></dd>
The total number of trials conducted.
</p></dd>
<dt><span class="term">successes</span></dt>
<dd><p>
The number of successes that occurred.
</p></dd>
The number of successes that occurred.
</p></dd>
<dt><span class="term">alpha</span></dt>
<dd><p>
The largest acceptable probability that the true value of the success
fraction is <span class="bold"><strong>greater than</strong></span> the value
returned.
</p></dd>
The largest acceptable probability that the true value of the success
fraction is <span class="bold"><strong>greater than</strong></span> the value
returned.
</p></dd>
</dl>
</div>
<p>
@@ -358,7 +358,7 @@
vol. 48, no3, 605-621</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures"></a><h6>
<a name="id910980"></a>
<a name="id878589"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_at_least_a_certain_number_of_failures">Estimating
Number of Trials to Ensure at Least a Certain Number of Failures</a>
</h6>
@@ -376,17 +376,17 @@
<dl>
<dt><span class="term">k</span></dt>
<dd><p>
The target number of failures to be observed.
</p></dd>
The target number of failures to be observed.
</p></dd>
<dt><span class="term">p</span></dt>
<dd><p>
The probability of <span class="emphasis"><em>success</em></span> for each trial.
</p></dd>
The probability of <span class="emphasis"><em>success</em></span> for each trial.
</p></dd>
<dt><span class="term">alpha</span></dt>
<dd><p>
The maximum acceptable risk that only k failures or fewer will be
observed.
</p></dd>
The maximum acceptable risk that only k failures or fewer will
be observed.
</p></dd>
</dl>
</div>
<p>
@@ -409,7 +409,7 @@
probability of observing k failures or fewer.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less"></a><h6>
<a name="id911201"></a>
<a name="id878868"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.estimating_number_of_trials_to_ensure_a_maximum_number_of_failures_or_less">Estimating
Number of Trials to Ensure a Maximum Number of Failures or Less</a>
</h6>
@@ -428,17 +428,17 @@
<dl>
<dt><span class="term">k</span></dt>
<dd><p>
The maximum number of failures to be observed.
</p></dd>
The maximum number of failures to be observed.
</p></dd>
<dt><span class="term">p</span></dt>
<dd><p>
The probability of <span class="emphasis"><em>success</em></span> for each trial.
</p></dd>
The probability of <span class="emphasis"><em>success</em></span> for each trial.
</p></dd>
<dt><span class="term">alpha</span></dt>
<dd><p>
The maximum acceptable <span class="emphasis"><em>risk</em></span> that more than k
failures will be observed.
</p></dd>
The maximum acceptable <span class="emphasis"><em>risk</em></span> that more than
k failures will be observed.
</p></dd>
</dl>
</div>
<p>
@@ -457,7 +457,7 @@
probability of observing more than k failures.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.non_member_accessors"></a><h5>
<a name="id911429"></a>
<a name="id879154"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -478,7 +478,7 @@
in the context of this distribution:
</p>
<div class="table">
<a name="id911522"></a><p class="title"><b>Table&#160;12.&#160;Meaning of the non-member accessors.</b></p>
<a name="id879296"></a><p class="title"><b>Table&#160;12.&#160;Meaning of the non-member accessors.</b></p>
<div class="table-contents"><table class="table" summary="Meaning of the non-member accessors.">
<colgroup>
<col>
@@ -486,124 +486,127 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
</th>
<p>
Function
</p>
</th>
<th>
<p>
Meaning
</p>
</th>
<p>
Meaning
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>
</p>
</td>
<p>
<a class="link" href="../nmp.html#math.dist.pdf">Probability Density Function</a>
</p>
</td>
<td>
<p>
The probability of obtaining <span class="bold"><strong>exactly k failures</strong></span>
from k+r trials with success fraction p. For example:
</p>
<p>
<p>
The probability of obtaining <span class="bold"><strong>exactly
k failures</strong></span> from k+r trials with success fraction
p. For example:
</p>
<p>
</p>
<pre class="programlisting"><span class="identifier">pdf</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">)</span></pre>
<p>
</p>
</td>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>
</p>
</td>
<p>
<a class="link" href="../nmp.html#math.dist.cdf">Cumulative Distribution Function</a>
</p>
</td>
<td>
<p>
The probability of obtaining <span class="bold"><strong>k failures or
fewer</strong></span> from k+r trials with success fraction p and success
on the last trial. For example:
</p>
<p>
<p>
The probability of obtaining <span class="bold"><strong>k failures
or fewer</strong></span> from k+r trials with success fraction p
and success on the last trial. For example:
</p>
<p>
</p>
<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">)</span></pre>
<p>
</p>
</td>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../nmp.html#math.dist.ccdf">Complement of the Cumulative Distribution
Function</a>
</p>
</td>
<p>
<a class="link" href="../nmp.html#math.dist.ccdf">Complement of the Cumulative
Distribution Function</a>
</p>
</td>
<td>
<p>
The probability of obtaining <span class="bold"><strong>more than k
failures</strong></span> from k+r trials with success fraction p and
success on the last trial. For example:
</p>
<p>
<p>
The probability of obtaining <span class="bold"><strong>more than
k failures</strong></span> from k+r trials with success fraction
p and success on the last trial. For example:
</p>
<p>
</p>
<pre class="programlisting"><span class="identifier">cdf</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">k</span><span class="special">))</span></pre>
<p>
</p>
</td>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>
</p>
</td>
<p>
<a class="link" href="../nmp.html#math.dist.quantile">Quantile</a>
</p>
</td>
<td>
<p>
The <span class="bold"><strong>greatest</strong></span> number of failures
k expected to be observed from k+r trials with success fraction
p, at probability P. Note that the value returned is a real-number,
and not an integer. Depending on the use case you may want to take
either the floor or ceiling of the real result. For example:
</p>
<p>
<p>
The <span class="bold"><strong>greatest</strong></span> number of failures
k expected to be observed from k+r trials with success fraction
p, at probability P. Note that the value returned is a real-number,
and not an integer. Depending on the use case you may want
to take either the floor or ceiling of the real result. For
example:
</p>
<p>
</p>
<pre class="programlisting"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">P</span><span class="special">)</span></pre>
<p>
</p>
</td>
</p>
</td>
</tr>
<tr>
<td>
<p>
<a class="link" href="../nmp.html#math.dist.quantile_c">Quantile from the complement
of the probability</a>
</p>
</td>
<p>
<a class="link" href="../nmp.html#math.dist.quantile_c">Quantile from the complement
of the probability</a>
</p>
</td>
<td>
<p>
The <span class="bold"><strong>smallest</strong></span> number of failures
k expected to be observed from k+r trials with success fraction
p, at probability P. Note that the value returned is a real-number,
and not an integer. Depending on the use case you may want to take
either the floor or ceiling of the real result. For example:
<p>
The <span class="bold"><strong>smallest</strong></span> number of failures
k expected to be observed from k+r trials with success fraction
p, at probability P. Note that the value returned is a real-number,
and not an integer. Depending on the use case you may want
to take either the floor or ceiling of the real result. For
example:
</p>
<pre class="programlisting"><span class="identifier">quantile</span><span class="special">(</span><span class="identifier">complement</span><span class="special">(</span><span class="identifier">negative_binomial</span><span class="special">(</span><span class="identifier">r</span><span class="special">,</span> <span class="identifier">p</span><span class="special">),</span> <span class="identifier">P</span><span class="special">))</span></pre>
<p>
</p>
</td>
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy"></a><h5>
<a name="id911934"></a>
<a name="id879799"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -613,7 +616,7 @@
please refer to these functions for information on accuracy.
</p>
<a name="math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation"></a><h5>
<a name="id911960"></a>
<a name="id879844"></a>
<a class="link" href="negative_binomial_dist.html#math_toolkit.dist.dist_ref.dists.negative_binomial_dist.implementation">Implementation</a>
</h5>
<p>
@@ -629,249 +632,252 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
pdf = exp(lgamma(r + k) - lgamma(r) - lgamma(k+1)) * pow(p, r)
* pow((1-p), k)
</p>
<p>
Implementation is in terms of <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>:
</p>
<p>
(p/(r + k)) * ibeta_derivative(r, static_cast&lt;RealType&gt;(k+1),
p) The function <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>
is used here, since it has already been optimised for the lowest
possible error - indeed this is really just a thin wrapper around
part of the internals of the incomplete beta function.
</p>
<p>
pdf = exp(lgamma(r + k) - lgamma(r) - lgamma(k+1)) * pow(p,
r) * pow((1-p), k)
</p>
<p>
Implementation is in terms of <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>:
</p>
<p>
(p/(r + k)) * ibeta_derivative(r, static_cast&lt;RealType&gt;(k+1),
p) The function <a class="link" href="../../../special/sf_beta/beta_derivative.html" title="Derivative of the Incomplete Beta Function">ibeta_derivative</a>
is used here, since it has already been optimised for the lowest
possible error - indeed this is really just a thin wrapper
around part of the internals of the incomplete beta function.
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
cdf = I<sub>p</sub>(r, k+1) = ibeta(r, k+1, p)
</p>
<p>
= ibeta(r, static_cast&lt;RealType&gt;(k+1), p)
</p>
<p>
Using the relation:
</p>
<p>
cdf = I<sub>p</sub>(r, k+1) = ibeta(r, k+1, p)
</p>
<p>
= ibeta(r, static_cast&lt;RealType&gt;(k+1), p)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation:
</p>
<p>
1 - cdf = I<sub>p</sub>(k+1, r)
</p>
<p>
= ibetac(r, static_cast&lt;RealType&gt;(k+1), p)
</p>
<p>
Using the relation:
</p>
<p>
1 - cdf = I<sub>p</sub>(k+1, r)
</p>
<p>
= ibetac(r, static_cast&lt;RealType&gt;(k+1), p)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
ibeta_invb(r, p, P) - 1
</p>
<p>
ibeta_invb(r, p, P) - 1
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
ibetac_invb(r, p, Q) -1)
</p>
<p>
ibetac_invb(r, p, Q) -1)
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">r</span><span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">)/</span><span class="identifier">p</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">r</span><span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">)/</span><span class="identifier">p</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">r</span> <span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">)</span>
<span class="special">/</span> <span class="identifier">p</span>
<span class="special">*</span> <span class="identifier">p</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">r</span> <span class="special">(</span><span class="number">1</span><span class="special">-</span><span class="identifier">p</span><span class="special">)</span>
<span class="special">/</span> <span class="identifier">p</span>
<span class="special">*</span> <span class="identifier">p</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="identifier">floor</span><span class="special">((</span><span class="identifier">r</span><span class="special">-</span><span class="number">1</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span><span class="number">1</span> <span class="special">-</span> <span class="identifier">p</span><span class="special">)/</span><span class="identifier">p</span><span class="special">)</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">floor</span><span class="special">((</span><span class="identifier">r</span><span class="special">-</span><span class="number">1</span><span class="special">)</span>
<span class="special">*</span> <span class="special">(</span><span class="number">1</span> <span class="special">-</span>
<span class="identifier">p</span><span class="special">)/</span><span class="identifier">p</span><span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="special">(</span><span class="number">2</span>
<span class="special">-</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
<span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">r</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">p</span><span class="special">))</span></code>
</p>
<p>
<code class="computeroutput"><span class="special">(</span><span class="number">2</span>
<span class="special">-</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
<span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">r</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">p</span><span class="special">))</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">6</span> <span class="special">/</span>
<span class="identifier">r</span> <span class="special">+</span>
<span class="special">(</span><span class="identifier">p</span>
<span class="special">*</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
<span class="identifier">r</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">p</span>
<span class="special">)</span></code>
</p>
<p>
<code class="computeroutput"><span class="number">6</span> <span class="special">/</span>
<span class="identifier">r</span> <span class="special">+</span>
<span class="special">(</span><span class="identifier">p</span>
<span class="special">*</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
<span class="identifier">r</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">p</span>
<span class="special">)</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
<code class="computeroutput"><span class="number">6</span> <span class="special">/</span>
<span class="identifier">r</span> <span class="special">+</span>
<span class="special">(</span><span class="identifier">p</span>
<span class="special">*</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
<span class="identifier">r</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">p</span>
<span class="special">)</span> <span class="special">-</span><span class="number">3</span></code>
</p>
<p>
<code class="computeroutput"><span class="number">6</span> <span class="special">/</span>
<span class="identifier">r</span> <span class="special">+</span>
<span class="special">(</span><span class="identifier">p</span>
<span class="special">*</span> <span class="identifier">p</span><span class="special">)</span> <span class="special">/</span>
<span class="identifier">r</span> <span class="special">*</span>
<span class="special">(</span><span class="number">1</span>
<span class="special">-</span> <span class="identifier">p</span>
<span class="special">)</span> <span class="special">-</span><span class="number">3</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
parameter estimation member functions
</p>
<p>
parameter estimation member functions
</p>
</td>
<td>
<p>
</p>
<p>
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">find_lower_bound_on_p</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">find_lower_bound_on_p</span></code>
</p>
</td>
<td>
<p>
ibeta_inv(successes, failures + 1, alpha)
</p>
<p>
ibeta_inv(successes, failures + 1, alpha)
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">find_upper_bound_on_p</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">find_upper_bound_on_p</span></code>
</p>
</td>
<td>
<p>
ibetac_inv(successes, failures, alpha) plus see comments in code.
</p>
<p>
ibetac_inv(successes, failures, alpha) plus see comments in
code.
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">find_minimum_number_of_trials</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">find_minimum_number_of_trials</span></code>
</p>
</td>
<td>
<p>
ibeta_inva(k + 1, p, alpha)
</p>
<p>
ibeta_inva(k + 1, p, alpha)
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">find_maximum_number_of_trials</span></code>
</p>
<p>
<code class="computeroutput"><span class="identifier">find_maximum_number_of_trials</span></code>
</p>
</td>
<td>
<p>
ibetac_inva(k + 1, p, alpha)
</p>
<p>
ibetac_inva(k + 1, p, alpha)
</p>
</td>
</tr>
</tbody>
@@ -879,17 +885,17 @@
<p>
Implementation notes:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
The real concept type (that deliberately lacks the Lanczos approximation),
was found to take several minutes to evaluate some extreme test values,
so the test has been disabled for this type.
</li>
<li>
Much greater speed, and perhaps greater accuracy, might be achieved
for extreme values by using a normal approximation. This is NOT been
tested or implemented.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
The real concept type (that deliberately lacks the Lanczos approximation),
was found to take several minutes to evaluate some extreme test values,
so the test has been disabled for this type.
</li>
<li class="listitem">
Much greater speed, and perhaps greater accuracy, might be achieved
for extreme values by using a normal approximation. This is NOT been
tested or implemented.
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -904,7 +910,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="lognormal_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="nc_beta_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="lognormal_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="nc_beta_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Normal (Gaussian) Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="nc_t_dist.html" title="Noncentral T Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="nc_t_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pareto.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="nc_t_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="pareto.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.normal_dist"></a><a class="link" href="normal_dist.html" title="Normal (Gaussian) Distribution"> Normal
(Gaussian) Distribution</a>
@@ -79,7 +79,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/normal_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.normal_dist.member_functions"></a><h5>
<a name="id923329"></a>
<a name="id888981"></a>
<a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.member_functions">Member
Functions</a>
</h5>
@@ -109,7 +109,7 @@
be used generically).
</p>
<a name="math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors"></a><h5>
<a name="id923524"></a>
<a name="id889224"></a>
<a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -131,7 +131,7 @@
and complement cdf -&#8734; = 1 and +&#8734; = 0, if RealType permits.
</p>
<a name="math_toolkit.dist.dist_ref.dists.normal_dist.accuracy"></a><h5>
<a name="id923622"></a>
<a name="id889362"></a>
<a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -139,7 +139,7 @@
function</a>, and as such should have very low error rates.
</p>
<a name="math_toolkit.dist.dist_ref.dists.normal_dist.implementation"></a><h5>
<a name="id923647"></a>
<a name="id889406"></a>
<a class="link" href="normal_dist.html#math_toolkit.dist.dist_ref.dists.normal_dist.implementation">Implementation</a>
</h5>
<p>
@@ -153,135 +153,135 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = e<sup>-(x-m)<sup>2</sup>/(2s<sup>2</sup>)</sup> / (s * sqrt(2*pi))
</p>
<p>
Using the relation: pdf = e<sup>-(x-m)<sup>2</sup>/(2s<sup>2</sup>)</sup> / (s * sqrt(2*pi))
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: p = 0.5 * <a class="link" href="../../../special/sf_erf/error_function.html" title="Error Functions">erfc</a>(-(x-m)/(s*sqrt(2)))
</p>
<p>
Using the relation: p = 0.5 * <a class="link" href="../../../special/sf_erf/error_function.html" title="Error Functions">erfc</a>(-(x-m)/(s*sqrt(2)))
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = 0.5 * <a class="link" href="../../../special/sf_erf/error_function.html" title="Error Functions">erfc</a>((x-m)/(s*sqrt(2)))
</p>
<p>
Using the relation: q = 0.5 * <a class="link" href="../../../special/sf_erf/error_function.html" title="Error Functions">erfc</a>((x-m)/(s*sqrt(2)))
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: x = m - s * sqrt(2) * <a class="link" href="../../../special/sf_erf/error_inv.html" title="Error Function Inverses">erfc_inv</a>(2*p)
</p>
<p>
Using the relation: x = m - s * sqrt(2) * <a class="link" href="../../../special/sf_erf/error_inv.html" title="Error Function Inverses">erfc_inv</a>(2*p)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: x = m + s * sqrt(2) * <a class="link" href="../../../special/sf_erf/error_inv.html" title="Error Function Inverses">erfc_inv</a>(2*p)
</p>
<p>
Using the relation: x = m + s * sqrt(2) * <a class="link" href="../../../special/sf_erf/error_inv.html" title="Error Function Inverses">erfc_inv</a>(2*p)
</p>
</td>
</tr>
<tr>
<td>
<p>
mean and standard deviation
</p>
<p>
mean and standard deviation
</p>
</td>
<td>
<p>
The same as <code class="computeroutput"><span class="identifier">dist</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span></code> and <code class="computeroutput"><span class="identifier">dist</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span></code>
</p>
<p>
The same as <code class="computeroutput"><span class="identifier">dist</span><span class="special">.</span><span class="identifier">mean</span><span class="special">()</span></code> and <code class="computeroutput"><span class="identifier">dist</span><span class="special">.</span><span class="identifier">standard_deviation</span><span class="special">()</span></code>
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
The same as the mean.
</p>
<p>
The same as the mean.
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
0
</p>
<p>
0
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
3
</p>
<p>
3
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
0
</p>
<p>
0
</p>
</td>
</tr>
</tbody>
@@ -299,7 +299,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="nc_t_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="pareto.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="nc_t_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="pareto.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Pareto Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="normal_dist.html" title="Normal (Gaussian) Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="normal_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="poisson_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="normal_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="poisson_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.pareto"></a><a class="link" href="pareto.html" title="Pareto Distribution"> Pareto
Distribution</a>
@@ -87,12 +87,12 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/pareto_pdf2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.pareto.related_distributions"></a><h5>
<a name="id924420"></a>
<a name="id890250"></a>
<a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.related_distributions">Related
distributions</a>
</h5>
<a name="math_toolkit.dist.dist_ref.dists.pareto.member_functions"></a><h5>
<a name="id924438"></a>
<a name="id890350"></a>
<a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.member_functions">Member
Functions</a>
</h5>
@@ -118,7 +118,7 @@
Returns the <span class="emphasis"><em>shape</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors"></a><h5>
<a name="id924606"></a>
<a name="id890552"></a>
<a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -138,7 +138,7 @@
The supported domain of the random variable is [scale, &#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.pareto.accuracy"></a><h5>
<a name="id924705"></a>
<a name="id890691"></a>
<a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.accuracy">Accuracy</a>
</h5>
<p>
@@ -151,7 +151,7 @@
zero) see also <a class="link" href="../../stat_tut/overview/complements.html#why_complements">why complements?</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.pareto.implementation"></a><h5>
<a name="id924742"></a>
<a name="id890762"></a>
<a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.implementation">Implementation</a>
</h5>
<p>
@@ -167,172 +167,176 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf p = &#945;&#946;<sup>&#945;</sup>/x<sup>&#945; +1</sup>
</p>
<p>
Using the relation: pdf p = &#945;&#946;<sup>&#945;</sup>/x<sup>&#945; +1</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: cdf p = 1 - (&#946; / x)<sup>&#945;</sup>
</p>
<p>
Using the relation: cdf p = 1 - (&#946; / x)<sup>&#945;</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = 1 - p = -(&#946; / x)<sup>&#945;</sup>
</p>
<p>
Using the relation: q = 1 - p = -(&#946; / x)<sup>&#945;</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: x = &#946; / (1 - p)<sup>1/&#945;</sup>
</p>
<p>
Using the relation: x = &#946; / (1 - p)<sup>1/&#945;</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: x = &#946; / (q)<sup>1/&#945;</sup>
</p>
<p>
Using the relation: x = &#946; / (q)<sup>1/&#945;</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
&#945;&#946; / (&#946; - 1)
</p>
<p>
&#945;&#946; / (&#946; - 1)
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
&#946;&#945;<sup>2</sup> / (&#946; - 1)<sup>2</sup> (&#946; - 2)
</p>
<p>
&#946;&#945;<sup>2</sup> / (&#946; - 1)<sup>2</sup> (&#946; - 2)
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
&#945;
</p>
<p>
&#945;
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
Refer to <a href="http://mathworld.wolfram.com/ParetoDistribution.html" target="_top">Weisstein,
Eric W. "Pareto Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
<p>
Refer to <a href="http://mathworld.wolfram.com/ParetoDistribution.html" target="_top">Weisstein,
Eric W. "Pareto Distribution." From MathWorld--A
Wolfram Web Resource.</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
Refer to <a href="http://mathworld.wolfram.com/ParetoDistribution.html" target="_top">Weisstein,
Eric W. "Pareto Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
<p>
Refer to <a href="http://mathworld.wolfram.com/ParetoDistribution.html" target="_top">Weisstein,
Eric W. "Pareto Distribution." From MathWorld--A
Wolfram Web Resource.</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
Refer to <a href="http://mathworld.wolfram.com/ParetoDistribution.html" target="_top">Weisstein,
Eric W. "pareto Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
<p>
Refer to <a href="http://mathworld.wolfram.com/ParetoDistribution.html" target="_top">Weisstein,
Eric W. "pareto Distribution." From MathWorld--A
Wolfram Web Resource.</a>
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.pareto.references"></a><h5>
<a name="id925067"></a>
<a name="id891369"></a>
<a class="link" href="pareto.html#math_toolkit.dist.dist_ref.dists.pareto.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li><a href="http://en.wikipedia.org/wiki/pareto_distribution" target="_top">Pareto
Distribution</a></li>
<li><a href="http://mathworld.wolfram.com/paretoDistribution.html" target="_top">Weisstein,
Eric W. "Pareto Distribution." From MathWorld--A Wolfram
Web Resource.</a></li>
<li>
Handbook of Statistical Distributions with Applications, K Krishnamoorthy,
ISBN 1-58488-635-8, Chapter 23, pp 257 - 267. (Note the meaning of
a and b is reversed in Wolfram and Krishnamoorthy).
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a href="http://en.wikipedia.org/wiki/pareto_distribution" target="_top">Pareto
Distribution</a>
</li>
<li class="listitem">
<a href="http://mathworld.wolfram.com/paretoDistribution.html" target="_top">Weisstein,
Eric W. "Pareto Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</li>
<li class="listitem">
Handbook of Statistical Distributions with Applications, K Krishnamoorthy,
ISBN 1-58488-635-8, Chapter 23, pp 257 - 267. (Note the meaning of
a and b is reversed in Wolfram and Krishnamoorthy).
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -347,7 +351,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="normal_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="poisson_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
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@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Poisson Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="pareto.html" title="Pareto Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="pareto.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="rayleigh.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist"></a><a class="link" href="poisson_dist.html" title="Poisson Distribution"> Poisson
Distribution</a>
@@ -86,7 +86,7 @@
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../../doc/html/images/caution.png"></td>
<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">
@@ -122,7 +122,7 @@
<p>
</p>
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions"></a><h5>
<a name="id925589"></a>
<a name="id892046"></a>
<a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.member_functions">Member
Functions</a>
</h5>
@@ -137,7 +137,7 @@
Returns the <span class="emphasis"><em>mean</em></span> of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors"></a><h5>
<a name="id925678"></a>
<a name="id892157"></a>
<a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -157,7 +157,7 @@
The domain of the random variable is [0, &#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy"></a><h5>
<a name="id925775"></a>
<a name="id892305"></a>
<a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -171,7 +171,7 @@
using an iterative method with a lower tolerance to avoid excessive computation.
</p>
<a name="math_toolkit.dist.dist_ref.dists.poisson_dist.implementation"></a><h5>
<a name="id925804"></a>
<a name="id892356"></a>
<a class="link" href="poisson_dist.html#math_toolkit.dist.dist_ref.dists.poisson_dist.implementation">Implementation</a>
</h5>
<p>
@@ -186,139 +186,139 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = e<sup>-&#955;</sup> &#955;<sup>k</sup> / k!
</p>
<p>
Using the relation: pdf = e<sup>-&#955;</sup> &#955;<sup>k</sup> / k!
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: p = &#915;(k+1, &#955;) / k! = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>(k+1,
&#955;)
</p>
<p>
Using the relation: p = &#915;(k+1, &#955;) / k! = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_q</a>(k+1,
&#955;)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>(k+1,
&#955;)
</p>
<p>
Using the relation: q = <a class="link" href="../../../special/sf_gamma/igamma.html" title="Incomplete Gamma Functions">gamma_p</a>(k+1,
&#955;)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: k = <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a>(&#955;,
p) - 1
</p>
<p>
Using the relation: k = <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_q_inva</a>(&#955;,
p) - 1
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: k = <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a>(&#955;,
q) - 1
</p>
<p>
Using the relation: k = <a class="link" href="../../../special/sf_gamma/igamma_inv.html" title="Incomplete Gamma Function Inverses">gamma_p_inva</a>(&#955;,
q) - 1
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
&#955;
</p>
<p>
&#955;
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
floor (&#955;) or &#8970;&#955;&#8971;
</p>
<p>
floor (&#955;) or &#8970;&#955;&#8971;
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
1/&#8730;&#955;
</p>
<p>
1/&#8730;&#955;
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
3 + 1/&#955;
</p>
<p>
3 + 1/&#955;
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
1/&#955;
</p>
<p>
1/&#955;
</p>
</td>
</tr>
</tbody>
@@ -336,7 +336,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="pareto.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="rayleigh.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</body>
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View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Rayleigh Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="poisson_dist.html" title="Poisson Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="poisson_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="students_t_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="poisson_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="students_t_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.rayleigh"></a><a class="link" href="rayleigh.html" title="Rayleigh Distribution"> Rayleigh
Distribution</a>
@@ -86,7 +86,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/rayleigh_cdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions"></a><h5>
<a name="id926511"></a>
<a name="id893128"></a>
<a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.related_distributions">Related
distributions</a>
</h5>
@@ -102,7 +102,7 @@
distribution</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.member_functions"></a><h5>
<a name="id926562"></a>
<a name="id893222"></a>
<a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.member_functions">Member
Functions</a>
</h5>
@@ -121,7 +121,7 @@
Returns the <span class="emphasis"><em>sigma</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors"></a><h5>
<a name="id926665"></a>
<a name="id893403"></a>
<a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -141,7 +141,7 @@
The domain of the random variable is [0, max_value].
</p>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.accuracy"></a><h5>
<a name="id926765"></a>
<a name="id893551"></a>
<a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.accuracy">Accuracy</a>
</h5>
<p>
@@ -151,7 +151,7 @@
using NTL RR type with 150-bit accuracy, about 50 decimal digits.
</p>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.implementation"></a><h5>
<a name="id926799"></a>
<a name="id893603"></a>
<a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.implementation">Implementation</a>
</h5>
<p>
@@ -166,168 +166,172 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = x * exp(-x<sup>2</sup>)/2 &#963;<sup>2</sup>
</p>
<p>
Using the relation: pdf = x * exp(-x<sup>2</sup>)/2 &#963;<sup>2</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: p = 1 - exp(-x<sup>2</sup>/2) &#963;<sup>2</sup> = -<a class="link" href="../../../special/powers/expm1.html" title="expm1">expm1</a>(-x<sup>2</sup>/2)
&#963;<sup>2</sup>
</p>
<p>
Using the relation: p = 1 - exp(-x<sup>2</sup>/2) &#963;<sup>2</sup> = -<a class="link" href="../../../special/powers/expm1.html" title="expm1">expm1</a>(-x<sup>2</sup>/2)
&#963;<sup>2</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = exp(-x<sup>2</sup>/ 2) * &#963;<sup>2</sup>
</p>
<p>
Using the relation: q = exp(-x<sup>2</sup>/ 2) * &#963;<sup>2</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: x = sqrt(-2 * &#963; <sup>2</sup>) * log(1 - p)) = sqrt(-2
* &#963; <sup>2</sup>) * <a class="link" href="../../../special/powers/log1p.html" title="log1p">log1p</a>(-p))
</p>
<p>
Using the relation: x = sqrt(-2 * &#963; <sup>2</sup>) * log(1 - p)) = sqrt(-2
* &#963; <sup>2</sup>) * <a class="link" href="../../../special/powers/log1p.html" title="log1p">log1p</a>(-p))
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: x = sqrt(-2 * &#963; <sup>2</sup>) * log(q))
</p>
<p>
Using the relation: x = sqrt(-2 * &#963; <sup>2</sup>) * log(q))
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
&#963; * sqrt(&#960;/2)
</p>
<p>
&#963; * sqrt(&#960;/2)
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
&#963;<sup>2</sup> * (4 - &#960;/2)
</p>
<p>
&#963;<sup>2</sup> * (4 - &#960;/2)
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
&#963;
</p>
<p>
&#963;
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
Constant from <a href="http://mathworld.wolfram.com/RayleighDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
<p>
Constant from <a href="http://mathworld.wolfram.com/RayleighDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A
Wolfram Web Resource.</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
Constant from <a href="http://mathworld.wolfram.com/RayleighDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
<p>
Constant from <a href="http://mathworld.wolfram.com/RayleighDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A
Wolfram Web Resource.</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
Constant from <a href="http://mathworld.wolfram.com/RayleighDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
<p>
Constant from <a href="http://mathworld.wolfram.com/RayleighDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A
Wolfram Web Resource.</a>
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.rayleigh.references"></a><h5>
<a name="id929884"></a>
<a name="id893967"></a>
<a class="link" href="rayleigh.html#math_toolkit.dist.dist_ref.dists.rayleigh.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li><a href="http://en.wikipedia.org/wiki/Rayleigh_distribution" target="_top">http://en.wikipedia.org/wiki/Rayleigh_distribution</a></li>
<li><a href="http://mathworld.wolfram.com/RayleighDistribution.html" target="_top">Weisstein,
Eric W. "Rayleigh Distribution." From MathWorld--A Wolfram
Web Resource.</a></li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a href="http://en.wikipedia.org/wiki/Rayleigh_distribution" target="_top">http://en.wikipedia.org/wiki/Rayleigh_distribution</a>
</li>
<li class="listitem">
<a href="http://mathworld.wolfram.com/RayleighDistribution.html" target="_top">Weisstein,
Eric W. "Rayleigh Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -342,7 +346,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="poisson_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="students_t_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="poisson_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="students_t_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
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@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Students t Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
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@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="rayleigh.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="triangular_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.students_t_dist"></a><a class="link" href="students_t_dist.html" title="Students t Distribution">
Students t Distribution</a>
@@ -97,7 +97,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/students_t_pdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.member_functions"></a><h5>
<a name="id930457"></a>
<a name="id894675"></a>
<a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.member_functions">Member
Functions</a>
</h5>
@@ -134,34 +134,34 @@
<dl>
<dt><span class="term">difference_from_mean</span></dt>
<dd><p>
The difference between the true mean and the sample mean that we
wish to show is significant.
</p></dd>
The difference between the true mean and the sample mean that we
wish to show is significant.
</p></dd>
<dt><span class="term">alpha</span></dt>
<dd><p>
The maximum acceptable probability of rejecting the null hypothesis
when it is in fact true.
</p></dd>
The maximum acceptable probability of rejecting the null hypothesis
when it is in fact true.
</p></dd>
<dt><span class="term">beta</span></dt>
<dd><p>
The maximum acceptable probability of failing to reject the null
hypothesis when it is in fact false.
</p></dd>
The maximum acceptable probability of failing to reject the null
hypothesis when it is in fact false.
</p></dd>
<dt><span class="term">sd</span></dt>
<dd><p>
The sample standard deviation.
</p></dd>
The sample standard deviation.
</p></dd>
<dt><span class="term">hint</span></dt>
<dd><p>
A hint for the location to start looking for the result, a good choice
for this would be the sample size of a previous borderline Student's
t test.
</p></dd>
A hint for the location to start looking for the result, a good
choice for this would be the sample size of a previous borderline
Student's t test.
</p></dd>
</dl>
</div>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../../../../../../doc/html/images/note.png"></td>
<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>
@@ -174,7 +174,7 @@
Engineering Statistics Handbook</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.non_member_accessors"></a><h5>
<a name="id930743"></a>
<a name="id895025"></a>
<a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -194,7 +194,7 @@
The domain of the random variable is [-&#8734;, +&#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.examples"></a><h5>
<a name="id930842"></a>
<a name="id895173"></a>
<a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.examples">Examples</a>
</h5>
<p>
@@ -202,7 +202,7 @@
are available illustrating the use of the Student's t distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.accuracy"></a><h5>
<a name="id930869"></a>
<a name="id895208"></a>
<a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -211,7 +211,7 @@
inverses</a>, refer to accuracy data on those functions for more information.
</p>
<a name="math_toolkit.dist.dist_ref.dists.students_t_dist.implementation"></a><h5>
<a name="id930900"></a>
<a name="id895253"></a>
<a class="link" href="students_t_dist.html#math_toolkit.dist.dist_ref.dists.students_t_dist.implementation">Implementation</a>
</h5>
<p>
@@ -226,181 +226,181 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = (v / (v + t<sup>2</sup>))<sup>(1+v)/2 </sup> / (sqrt(v) *
<a class="link" href="../../../special/sf_beta/beta_function.html" title="Beta">beta</a>(v/2,
0.5))
</p>
<p>
Using the relation: pdf = (v / (v + t<sup>2</sup>))<sup>(1+v)/2 </sup> / (sqrt(v)
* <a class="link" href="../../../special/sf_beta/beta_function.html" title="Beta">beta</a>(v/2,
0.5))
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relations:
</p>
<p>
p = 1 - z <span class="emphasis"><em>iff t &gt; 0</em></span>
</p>
<p>
p = z <span class="emphasis"><em>otherwise</em></span>
</p>
<p>
where z is given by:
</p>
<p>
<a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(v
/ 2, 0.5, v / (v + t<sup>2</sup>)) / 2 <span class="emphasis"><em>iff v &lt; 2t<sup>2</sup></em></span>
</p>
<p>
<a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>(0.5,
v / 2, t<sup>2 </sup> / (v + t<sup>2</sup>) / 2 <span class="emphasis"><em>otherwise</em></span>
</p>
<p>
Using the relations:
</p>
<p>
p = 1 - z <span class="emphasis"><em>iff t &gt; 0</em></span>
</p>
<p>
p = z <span class="emphasis"><em>otherwise</em></span>
</p>
<p>
where z is given by:
</p>
<p>
<a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibeta</a>(v
/ 2, 0.5, v / (v + t<sup>2</sup>)) / 2 <span class="emphasis"><em>iff v &lt; 2t<sup>2</sup></em></span>
</p>
<p>
<a class="link" href="../../../special/sf_beta/ibeta_function.html" title="Incomplete Beta Functions">ibetac</a>(0.5,
v / 2, t<sup>2 </sup> / (v + t<sup>2</sup>) / 2 <span class="emphasis"><em>otherwise</em></span>
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = cdf(-t)
</p>
<p>
Using the relation: q = cdf(-t)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: t = sign(p - 0.5) * sqrt(v * y / x)
</p>
<p>
where:
</p>
<p>
x = <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>(v
/ 2, 0.5, 2 * min(p, q))
</p>
<p>
y = 1 - x
</p>
<p>
The quantities <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>
are both returned by <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
without the subtraction implied above.
</p>
<p>
Using the relation: t = sign(p - 0.5) * sqrt(v * y / x)
</p>
<p>
where:
</p>
<p>
x = <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>(v
/ 2, 0.5, 2 * min(p, q))
</p>
<p>
y = 1 - x
</p>
<p>
The quantities <span class="emphasis"><em>x</em></span> and <span class="emphasis"><em>y</em></span>
are both returned by <a class="link" href="../../../special/sf_beta/ibeta_inv_function.html" title="The Incomplete Beta Function Inverses">ibeta_inv</a>
without the subtraction implied above.
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: t = -quantile(q)
</p>
<p>
Using the relation: t = -quantile(q)
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
0
</p>
<p>
0
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
v / (v - 2)
</p>
<p>
v / (v - 2)
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
0
</p>
<p>
0
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
0
</p>
<p>
0
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
3 * (v - 2) / (v - 4)
</p>
<p>
3 * (v - 2) / (v - 4)
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
6 / (df - 4)
</p>
<p>
6 / (df - 4)
</p>
</td>
</tr>
</tbody>
@@ -418,7 +418,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="rayleigh.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="triangular_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Triangular Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
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<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="students_t_dist.html" title="Students t Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="students_t_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="weibull.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="students_t_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="weibull.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.triangular_dist"></a><a class="link" href="triangular_dist.html" title="Triangular Distribution">
Triangular Distribution</a>
@@ -81,13 +81,13 @@
<p>
f(x) =
</p>
<div class="itemizedlist"><ul type="disc">
<li>
2(x-a)/(b-a) (c-a) for a &lt;= x &lt;= c
</li>
<li>
2(b-x)/(b-a)(b-c) for c &lt; x &lt;= b
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
2(x-a)/(b-a) (c-a) for a &lt;= x &lt;= c
</li>
<li class="listitem">
2(b-x)/(b-a)(b-c) for c &lt; x &lt;= b
</li>
</ul></div>
<p>
Parameter a (lower) can be any finite value. Parameter b (upper) can
@@ -128,7 +128,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/triangular_cdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.member_functions"></a><h5>
<a name="id931909"></a>
<a name="id896464"></a>
<a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.member_functions">Member
Functions</a>
</h5>
@@ -163,7 +163,7 @@
(default+1).
</p>
<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.non_member_accessors"></a><h5>
<a name="id932928"></a>
<a name="id896733"></a>
<a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -184,7 +184,7 @@
range is lower &lt;= x &lt;= upper.
</p>
<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.accuracy"></a><h5>
<a name="id933028"></a>
<a name="id896871"></a>
<a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -193,7 +193,7 @@
with arguments nearing the extremes of zero and unity.
</p>
<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.implementation"></a><h5>
<a name="id933049"></a>
<a name="id896913"></a>
<a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.implementation">Implementation</a>
</h5>
<p>
@@ -210,165 +210,165 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = 0 for x &lt; mode, 2(x-a)/(b-a)(c-a)
else 2*(b-x)/((b-a)(b-c))
</p>
<p>
Using the relation: pdf = 0 for x &lt; mode, 2(x-a)/(b-a)(c-a)
else 2*(b-x)/((b-a)(b-c))
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: cdf = 0 for x &lt; mode (x-a)<sup>2</sup>/((b-a)(c-a))
else 1 - (b-x)<sup>2</sup>/((b-a)(b-c))
</p>
<p>
Using the relation: cdf = 0 for x &lt; mode (x-a)<sup>2</sup>/((b-a)(c-a))
else 1 - (b-x)<sup>2</sup>/((b-a)(b-c))
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = 1 - p
</p>
<p>
Using the relation: q = 1 - p
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
let p0 = (c-a)/(b-a) the point of inflection on the cdf, then
given probability p and q = 1-p:
</p>
<p>
x = sqrt((b-a)(c-a)p) + a ; for p &lt; p0
</p>
<p>
x = c ; for p == p0
</p>
<p>
x = b - sqrt((b-a)(b-c)q) ; for p &gt; p0
</p>
<p>
(See <a href="../../../../../../../../../boost/math/distributions/triangular.hpp" target="_top">/boost/math/distributions/triangular.hpp</a>
for details.)
</p>
<p>
let p0 = (c-a)/(b-a) the point of inflection on the cdf, then
given probability p and q = 1-p:
</p>
<p>
x = sqrt((b-a)(c-a)p) + a ; for p &lt; p0
</p>
<p>
x = c ; for p == p0
</p>
<p>
x = b - sqrt((b-a)(b-c)q) ; for p &gt; p0
</p>
<p>
(See <a href="../../../../../../../../../boost/math/distributions/triangular.hpp" target="_top">/boost/math/distributions/triangular.hpp</a>
for details.)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
As quantile (See <a href="../../../../../../../../../boost/math/distributions/triangular.hpp" target="_top">/boost/math/distributions/triangular.hpp</a>
for details.)
</p>
<p>
As quantile (See <a href="../../../../../../../../../boost/math/distributions/triangular.hpp" target="_top">/boost/math/distributions/triangular.hpp</a>
for details.)
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
(a + b + 3) / 3
</p>
<p>
(a + b + 3) / 3
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
(a<sup>2</sup>+b<sup>2</sup>+c<sup>2</sup> - ab - ac - bc)/18
</p>
<p>
(a<sup>2</sup>+b<sup>2</sup>+c<sup>2</sup> - ab - ac - bc)/18
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
c
</p>
<p>
c
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
(See <a href="../../../../../../../../../boost/math/distributions/triangular.hpp" target="_top">/boost/math/distributions/triangular.hpp</a>
for details).
</p>
<p>
(See <a href="../../../../../../../../../boost/math/distributions/triangular.hpp" target="_top">/boost/math/distributions/triangular.hpp</a>
for details).
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
12/5
</p>
<p>
12/5
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
-3/5
</p>
<p>
-3/5
</p>
</td>
</tr>
</tbody>
@@ -378,28 +378,38 @@
Calculate and plot probability distributions</a>
</p>
<a name="math_toolkit.dist.dist_ref.dists.triangular_dist.references"></a><h5>
<a name="id933370"></a>
<a name="id897278"></a>
<a class="link" href="triangular_dist.html#math_toolkit.dist.dist_ref.dists.triangular_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li><a href="http://en.wikipedia.org/wiki/Triangular_distribution" target="_top">Wikpedia
triangular distribution</a></li>
<li><a href="http://mathworld.wolfram.com/TriangularDistribution.html" target="_top">Weisstein,
Eric W. "Triangular Distribution." From MathWorld--A Wolfram
Web Resource.</a></li>
<li>
Evans, M.; Hastings, N.; and Peacock, B. "Triangular Distribution."
Ch. 40 in Statistical Distributions, 3rd ed. New York: Wiley, pp. 187-188,
2000, ISBN - 0471371246]
</li>
<li><a href="http://www.brighton-webs.co.uk/distributions/triangular.asp" target="_top">Brighton
Webs Ltd. BW D-Calc 1.0 Distribution Calculator</a></li>
<li><a href="http://www.worldscibooks.com/mathematics/etextbook/5720/5720_chap1.pdf" target="_top">The
Triangular Distribution including its history.</a></li>
<li><a href="http://www.measurement.sk/2002/S1/Wimmer2.pdf" target="_top">Gejza Wimmer,
Viktor Witkovsky and Tomas Duby, Measurement Science Review, Volume
2, Section 1, 2002, Proper Rounding Of The Measurement Results Under
The Assumption Of Triangular Distribution.</a></li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a href="http://en.wikipedia.org/wiki/Triangular_distribution" target="_top">Wikpedia
triangular distribution</a>
</li>
<li class="listitem">
<a href="http://mathworld.wolfram.com/TriangularDistribution.html" target="_top">Weisstein,
Eric W. "Triangular Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</li>
<li class="listitem">
Evans, M.; Hastings, N.; and Peacock, B. "Triangular Distribution."
Ch. 40 in Statistical Distributions, 3rd ed. New York: Wiley, pp.
187-188, 2000, ISBN - 0471371246]
</li>
<li class="listitem">
<a href="http://www.brighton-webs.co.uk/distributions/triangular.asp" target="_top">Brighton
Webs Ltd. BW D-Calc 1.0 Distribution Calculator</a>
</li>
<li class="listitem">
<a href="http://www.worldscibooks.com/mathematics/etextbook/5720/5720_chap1.pdf" target="_top">The
Triangular Distribution including its history.</a>
</li>
<li class="listitem">
<a href="http://www.measurement.sk/2002/S1/Wimmer2.pdf" target="_top">Gejza
Wimmer, Viktor Witkovsky and Tomas Duby, Measurement Science Review,
Volume 2, Section 1, 2002, Proper Rounding Of The Measurement Results
Under The Assumption Of Triangular Distribution.</a>
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -414,7 +424,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="students_t_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="weibull.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Uniform Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="weibull.html" title="Weibull Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="weibull.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../dist_algorithms.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="weibull.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="../dist_algorithms.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.uniform_dist"></a><a class="link" href="uniform_dist.html" title="Uniform Distribution"> Uniform
Distribution</a>
@@ -67,20 +67,20 @@
<p>
f(x) =
</p>
<div class="itemizedlist"><ul type="disc">
<li>
1 / (upper - lower) for lower &lt; x &lt; upper
</li>
<li>
zero for x &lt; lower or x &gt; upper
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
1 / (upper - lower) for lower &lt; x &lt; upper
</li>
<li class="listitem">
zero for x &lt; lower or x &gt; upper
</li>
</ul></div>
<p>
and in this implementation:
</p>
<div class="itemizedlist"><ul type="disc"><li>
1 / (upper - lower) for x = lower or x = upper
</li></ul></div>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
1 / (upper - lower) for x = lower or x = upper
</li></ul></div>
<p>
The choice of x = lower or x = upper is made because statistical use
of this distribution judged is most likely: the method of maximum likelihood
@@ -117,7 +117,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/uniform_cdf.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.member_functions"></a><h5>
<a name="id936044"></a>
<a name="id899619"></a>
<a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.member_functions">Member
Functions</a>
</h5>
@@ -144,7 +144,7 @@
Returns the <span class="emphasis"><em>upper</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.non_member_accessors"></a><h5>
<a name="id936209"></a>
<a name="id899824"></a>
<a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -165,7 +165,7 @@
range is only <span class="emphasis"><em>lower</em></span> &lt;= x &lt;= <span class="emphasis"><em>upper</em></span>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.accuracy"></a><h5>
<a name="id936314"></a>
<a name="id899979"></a>
<a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.accuracy">Accuracy</a>
</h5>
<p>
@@ -173,7 +173,7 @@
and so should have errors within an epsilon or two.
</p>
<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.implementation"></a><h5>
<a name="id936333"></a>
<a name="id900007"></a>
<a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.implementation">Implementation</a>
</h5>
<p>
@@ -189,164 +189,170 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = 0 for x &lt; a, 1 / (b - a) for a &lt;=
x &lt;= b, 0 for x &gt; b
</p>
<p>
Using the relation: pdf = 0 for x &lt; a, 1 / (b - a) for a
&lt;= x &lt;= b, 0 for x &gt; b
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: cdf = 0 for x &lt; a, (x - a) / (b - a) for
a &lt;= x &lt;= b, 1 for x &gt; b
</p>
<p>
Using the relation: cdf = 0 for x &lt; a, (x - a) / (b - a)
for a &lt;= x &lt;= b, 1 for x &gt; b
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = 1 - p, (b - x) / (b - a)
</p>
<p>
Using the relation: q = 1 - p, (b - x) / (b - a)
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: x = p * (b - a) + a;
</p>
<p>
Using the relation: x = p * (b - a) + a;
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
x = -q * (b - a) + b
</p>
<p>
x = -q * (b - a) + b
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
(a + b) / 2
</p>
<p>
(a + b) / 2
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
(b - a) <sup>2</sup> / 12
</p>
<p>
(b - a) <sup>2</sup> / 12
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
any value in [a, b] but a is chosen. (Would NaN be better?)
</p>
<p>
any value in [a, b] but a is chosen. (Would NaN be better?)
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
0
</p>
<p>
0
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
-6/5 = -1.2 exactly. (kurtosis - 3)
</p>
<p>
-6/5 = -1.2 exactly. (kurtosis - 3)
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
9/5
</p>
<p>
9/5
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.uniform_dist.references"></a><h5>
<a name="id936597"></a>
<a name="id900092"></a>
<a class="link" href="uniform_dist.html#math_toolkit.dist.dist_ref.dists.uniform_dist.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li><a href="http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29" target="_top">Wikpedia
continuous uniform distribution</a></li>
<li><a href="http://mathworld.wolfram.com/UniformDistribution.html" target="_top">Weisstein,
Weisstein, Eric W. "Uniform Distribution." From MathWorld--A
Wolfram Web Resource.</a></li>
<li><a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3662.htm" target="_top">http://www.itl.nist.gov/div898/handbook/eda/section3/eda3662.htm</a></li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a href="http://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29" target="_top">Wikpedia
continuous uniform distribution</a>
</li>
<li class="listitem">
<a href="http://mathworld.wolfram.com/UniformDistribution.html" target="_top">Weisstein,
Weisstein, Eric W. "Uniform Distribution." From MathWorld--A
Wolfram Web Resource.</a>
</li>
<li class="listitem">
<a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3662.htm" target="_top">http://www.itl.nist.gov/div898/handbook/eda/section3/eda3662.htm</a>
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -361,7 +367,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="weibull.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../dist_algorithms.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
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</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Weibull Distribution</title>
<link rel="stylesheet" href="../../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Math Toolkit">
<link rel="up" href="../dists.html" title="Distributions">
<link rel="prev" href="triangular_dist.html" title="Triangular Distribution">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="triangular_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="uniform_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="triangular_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="uniform_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="math_toolkit.dist.dist_ref.dists.weibull"></a><a class="link" href="weibull.html" title="Weibull Distribution"> Weibull
Distribution</a>
@@ -72,18 +72,18 @@
in particular it can mimic distributions where the failure rate varies
over time. If the failure rate is:
</p>
<div class="itemizedlist"><ul type="disc">
<li>
constant over time, then &#945; = 1, suggests that items are failing from
random events.
</li>
<li>
decreases over time, then &#945; &lt; 1, suggesting "infant mortality".
</li>
<li>
increases over time, then &#945; &gt; 1, suggesting "wear out" -
more likely to fail as time goes by.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
constant over time, then &#945; = 1, suggests that items are failing from
random events.
</li>
<li class="listitem">
decreases over time, then &#945; &lt; 1, suggesting "infant mortality".
</li>
<li class="listitem">
increases over time, then &#945; &gt; 1, suggesting "wear out"
- more likely to fail as time goes by.
</li>
</ul></div>
<p>
The following graph illustrates how the PDF varies with the shape parameter
@@ -100,7 +100,7 @@
<span class="inlinemediaobject"><img src="../../../../../graphs/weibull_pdf2.png" align="middle"></span>
</p>
<a name="math_toolkit.dist.dist_ref.dists.weibull.related_distributions"></a><h5>
<a name="id933931"></a>
<a name="id897933"></a>
<a class="link" href="weibull.html#math_toolkit.dist.dist_ref.dists.weibull.related_distributions">Related
distributions</a>
</h5>
@@ -114,7 +114,7 @@
Distributions, Theory and Applications Samuel Kotz &amp; Saralees Nadarajah</a>.
</p>
<a name="math_toolkit.dist.dist_ref.dists.weibull.member_functions"></a><h5>
<a name="id933973"></a>
<a name="id898059"></a>
<a class="link" href="weibull.html#math_toolkit.dist.dist_ref.dists.weibull.member_functions">Member
Functions</a>
</h5>
@@ -140,7 +140,7 @@
Returns the <span class="emphasis"><em>scale</em></span> parameter of this distribution.
</p>
<a name="math_toolkit.dist.dist_ref.dists.weibull.non_member_accessors"></a><h5>
<a name="id934132"></a>
<a name="id898263"></a>
<a class="link" href="weibull.html#math_toolkit.dist.dist_ref.dists.weibull.non_member_accessors">Non-member
Accessors</a>
</h5>
@@ -160,7 +160,7 @@
The domain of the random variable is [0, &#8734;].
</p>
<a name="math_toolkit.dist.dist_ref.dists.weibull.accuracy"></a><h5>
<a name="id934231"></a>
<a name="id898412"></a>
<a class="link" href="weibull.html#math_toolkit.dist.dist_ref.dists.weibull.accuracy">Accuracy</a>
</h5>
<p>
@@ -170,7 +170,7 @@
as such should have very low error rates.
</p>
<a name="math_toolkit.dist.dist_ref.dists.weibull.implementation"></a><h5>
<a name="id934272"></a>
<a name="id898476"></a>
<a class="link" href="weibull.html#math_toolkit.dist.dist_ref.dists.weibull.implementation">Implementation</a>
</h5>
<p>
@@ -185,168 +185,174 @@
</colgroup>
<thead><tr>
<th>
<p>
Function
</p>
<p>
Function
</p>
</th>
<th>
<p>
Implementation Notes
</p>
<p>
Implementation Notes
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
pdf
</p>
<p>
pdf
</p>
</td>
<td>
<p>
Using the relation: pdf = &#945;&#946;<sup>-&#945; </sup>x<sup>&#945; - 1</sup> e<sup>-(x/beta)<sup>alpha</sup></sup>
</p>
<p>
Using the relation: pdf = &#945;&#946;<sup>-&#945; </sup>x<sup>&#945; - 1</sup> e<sup>-(x/beta)<sup>alpha</sup></sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf
</p>
<p>
cdf
</p>
</td>
<td>
<p>
Using the relation: p = -<a class="link" href="../../../special/powers/expm1.html" title="expm1">expm1</a>(-(x/&#946;)<sup>&#945;</sup>)
</p>
<p>
Using the relation: p = -<a class="link" href="../../../special/powers/expm1.html" title="expm1">expm1</a>(-(x/&#946;)<sup>&#945;</sup>)
</p>
</td>
</tr>
<tr>
<td>
<p>
cdf complement
</p>
<p>
cdf complement
</p>
</td>
<td>
<p>
Using the relation: q = e<sup>-(x/&#946;)<sup>&#945;</sup></sup>
</p>
<p>
Using the relation: q = e<sup>-(x/&#946;)<sup>&#945;</sup></sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile
</p>
<p>
quantile
</p>
</td>
<td>
<p>
Using the relation: x = &#946; * (-<a class="link" href="../../../special/powers/log1p.html" title="log1p">log1p</a>(-p))<sup>1/&#945;</sup>
</p>
<p>
Using the relation: x = &#946; * (-<a class="link" href="../../../special/powers/log1p.html" title="log1p">log1p</a>(-p))<sup>1/&#945;</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
quantile from the complement
</p>
<p>
quantile from the complement
</p>
</td>
<td>
<p>
Using the relation: x = &#946; * (-log(q))<sup>1/&#945;</sup>
</p>
<p>
Using the relation: x = &#946; * (-log(q))<sup>1/&#945;</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
mean
</p>
<p>
mean
</p>
</td>
<td>
<p>
&#946; * &#915;(1 + 1/&#945;)
</p>
<p>
&#946; * &#915;(1 + 1/&#945;)
</p>
</td>
</tr>
<tr>
<td>
<p>
variance
</p>
<p>
variance
</p>
</td>
<td>
<p>
&#946;<sup>2</sup>(&#915;(1 + 2/&#945;) - &#915;<sup>2</sup>(1 + 1/&#945;))
</p>
<p>
&#946;<sup>2</sup>(&#915;(1 + 2/&#945;) - &#915;<sup>2</sup>(1 + 1/&#945;))
</p>
</td>
</tr>
<tr>
<td>
<p>
mode
</p>
<p>
mode
</p>
</td>
<td>
<p>
&#946;((&#945; - 1) / &#945;)<sup>1/&#945;</sup>
</p>
<p>
&#946;((&#945; - 1) / &#945;)<sup>1/&#945;</sup>
</p>
</td>
</tr>
<tr>
<td>
<p>
skewness
</p>
<p>
skewness
</p>
</td>
<td>
<p>
Refer to <a href="http://mathworld.wolfram.com/WeibullDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
<p>
Refer to <a href="http://mathworld.wolfram.com/WeibullDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A
Wolfram Web Resource.</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis
</p>
<p>
kurtosis
</p>
</td>
<td>
<p>
Refer to <a href="http://mathworld.wolfram.com/WeibullDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
<p>
Refer to <a href="http://mathworld.wolfram.com/WeibullDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A
Wolfram Web Resource.</a>
</p>
</td>
</tr>
<tr>
<td>
<p>
kurtosis excess
</p>
<p>
kurtosis excess
</p>
</td>
<td>
<p>
Refer to <a href="http://mathworld.wolfram.com/WeibullDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</p>
<p>
Refer to <a href="http://mathworld.wolfram.com/WeibullDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A
Wolfram Web Resource.</a>
</p>
</td>
</tr>
</tbody>
</table></div>
<a name="math_toolkit.dist.dist_ref.dists.weibull.references"></a><h5>
<a name="id934585"></a>
<a name="id898838"></a>
<a class="link" href="weibull.html#math_toolkit.dist.dist_ref.dists.weibull.references">References</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li><a href="http://en.wikipedia.org/wiki/Weibull_distribution" target="_top">http://en.wikipedia.org/wiki/Weibull_distribution</a></li>
<li><a href="http://mathworld.wolfram.com/WeibullDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A Wolfram
Web Resource.</a></li>
<li><a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm" target="_top">Weibull
in NIST Exploratory Data Analysis</a></li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a href="http://en.wikipedia.org/wiki/Weibull_distribution" target="_top">http://en.wikipedia.org/wiki/Weibull_distribution</a>
</li>
<li class="listitem">
<a href="http://mathworld.wolfram.com/WeibullDistribution.html" target="_top">Weisstein,
Eric W. "Weibull Distribution." From MathWorld--A Wolfram
Web Resource.</a>
</li>
<li class="listitem">
<a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda3668.htm" target="_top">Weibull
in NIST Exploratory Data Analysis</a>
</li>
</ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
@@ -361,7 +367,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="triangular_dist.html"><img src="../../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.html"><img src="../../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="uniform_dist.html"><img src="../../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="triangular_dist.html"><img src="../../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dists.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="uniform_dist.html"><img src="../../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Non-Member Properties</title>
<link rel="stylesheet" href="../../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../index.html" title="Math Toolkit">
<link rel="up" href="../dist_ref.html" title="Statistical Distributions Reference">
<link rel="prev" href="../dist_ref.html" title="Statistical Distributions Reference">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../dist_ref.html"><img src="../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dists.html"><img src="../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="../dist_ref.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.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="dists.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.dist.dist_ref.nmp"></a><a class="link" href="nmp.html" title="Non-Member Properties"> Non-Member Properties</a>
</h4></div></div></div>
@@ -37,144 +37,152 @@
the function you want if you already know its name.
</p>
<a name="function_index"></a><a name="math_toolkit.dist.dist_ref.nmp.function_index"></a><h5>
<a name="id876728"></a>
<a name="id847334"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.function_index">Function
Index</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li>
<a class="link" href="nmp.html#math.dist.cdf">cdf</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.ccdf">cdf complement</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.chf">chf</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.hazard">hazard</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.kurtosis">kurtosis</a>.
</li>
<li><a class="link" href="nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a></li>
<li>
<a class="link" href="nmp.html#math.dist.mean">mean</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.median">median</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.mode">mode</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.pdf">pdf</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.range">range</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.quantile">quantile</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.quantile_c">quantile from the complement</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.skewness">skewness</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.sd">standard_deviation</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.support">support</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.variance">variance</a>.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a class="link" href="nmp.html#math.dist.cdf">cdf</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.ccdf">cdf complement</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.chf">chf</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.hazard">hazard</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.kurtosis">kurtosis</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.mean">mean</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.median">median</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.mode">mode</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.pdf">pdf</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.range">range</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.quantile">quantile</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.quantile_c">quantile from the complement</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.skewness">skewness</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.sd">standard_deviation</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.support">support</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.variance">variance</a>.
</li>
</ul></div>
<a name="concept_index"></a><a name="math_toolkit.dist.dist_ref.nmp.conceptual_index"></a><h5>
<a name="id876891"></a>
<a name="id847611"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.conceptual_index">Conceptual
Index</a>
</h5>
<div class="itemizedlist"><ul type="disc">
<li>
<a class="link" href="nmp.html#math.dist.ccdf">Complement of the Cumulative Distribution
Function</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.cdf">Cumulative Distribution Function</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.chf">Cumulative Hazard Function</a>.
</li>
<li>
<a class="link" href="nmp.html#cdf_inv">Inverse Cumulative Distribution Function</a>.
</li>
<li>
<a class="link" href="nmp.html#survival_inv">Inverse Survival Function</a>.
</li>
<li><a class="link" href="nmp.html#math.dist.hazard">Hazard Function</a></li>
<li>
<a class="link" href="nmp.html#lower_critical">Lower Critical Value</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.kurtosis">kurtosis</a>.
</li>
<li><a class="link" href="nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a></li>
<li>
<a class="link" href="nmp.html#math.dist.mean">mean</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.median">median</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.mode">mode</a>.
</li>
<li>
<a class="link" href="nmp.html#cdfPQ">P</a>.
</li>
<li>
<a class="link" href="nmp.html#percent">Percent Point Function</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.pdf">Probability Density Function</a>.
</li>
<li>
<a class="link" href="nmp.html#pmf">Probability Mass Function</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.range">range</a>.
</li>
<li>
<a class="link" href="nmp.html#cdfPQ">Q</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.quantile_c">Quantile from the complement of
the probability</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.skewness">skewness</a>.
</li>
<li><a class="link" href="nmp.html#math.dist.sd">standard deviation</a></li>
<li>
<a class="link" href="nmp.html#survival">Survival Function</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.support">support</a>.
</li>
<li>
<a class="link" href="nmp.html#upper_critical">Upper Critical Value</a>.
</li>
<li>
<a class="link" href="nmp.html#math.dist.variance">variance</a>.
</li>
<div class="itemizedlist"><ul class="itemizedlist" type="disc">
<li class="listitem">
<a class="link" href="nmp.html#math.dist.ccdf">Complement of the Cumulative Distribution
Function</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.cdf">Cumulative Distribution Function</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.chf">Cumulative Hazard Function</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#cdf_inv">Inverse Cumulative Distribution Function</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#survival_inv">Inverse Survival Function</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.hazard">Hazard Function</a>
</li>
<li class="listitem">
<a class="link" href="nmp.html#lower_critical">Lower Critical Value</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.kurtosis">kurtosis</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.kurtosis_excess">kurtosis_excess</a>
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.mean">mean</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.median">median</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.mode">mode</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#cdfPQ">P</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#percent">Percent Point Function</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.pdf">Probability Density Function</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#pmf">Probability Mass Function</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.range">range</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#cdfPQ">Q</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.quantile_c">Quantile from the complement of
the probability</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.skewness">skewness</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.sd">standard deviation</a>
</li>
<li class="listitem">
<a class="link" href="nmp.html#survival">Survival Function</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.support">support</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#upper_critical">Upper Critical Value</a>.
</li>
<li class="listitem">
<a class="link" href="nmp.html#math.dist.variance">variance</a>.
</li>
</ul></div>
<a name="math.dist.cdf"></a><a name="math_toolkit.dist.dist_ref.nmp.cumulative_distribution_function"></a><h5>
<a name="id877135"></a>
<a name="id848006"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.cumulative_distribution_function">Cumulative
Distribution Function</a>
</h5>
@@ -198,7 +206,7 @@
<span class="inlinemediaobject"><img src="../../../../graphs/cdf.png" alt="cdf"></span>
</p>
<a name="math.dist.ccdf"></a><a name="math_toolkit.dist.dist_ref.nmp.complement_of_the_cumulative_distribution_function"></a><h5>
<a name="id877305"></a>
<a name="id848225"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.complement_of_the_cumulative_distribution_function">Complement
of the Cumulative Distribution Function</a>
</h5>
@@ -239,7 +247,7 @@
complement is useful and when it should be used.
</p>
<a name="math.dist.hazard"></a><a name="math_toolkit.dist.dist_ref.nmp.hazard_function"></a><h5>
<a name="id877595"></a>
<a name="id848592"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.hazard_function">Hazard Function</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
@@ -258,7 +266,7 @@
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../doc/html/images/caution.png"></td>
<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>
@@ -267,7 +275,7 @@
</p></td></tr>
</table></div>
<a name="math.dist.chf"></a><a name="math_toolkit.dist.dist_ref.nmp.cumulative_hazard_function"></a><h5>
<a name="id877777"></a>
<a name="id848815"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.cumulative_hazard_function">Cumulative
Hazard Function</a>
</h5>
@@ -287,7 +295,7 @@
</p>
<div class="caution"><table border="0" summary="Caution">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Caution]" src="../../../../../../../../doc/html/images/caution.png"></td>
<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>
@@ -295,7 +303,7 @@
</p></td></tr>
</table></div>
<a name="math.dist.mean"></a><a name="math_toolkit.dist.dist_ref.nmp.mean"></a><h5>
<a name="id877959"></a>
<a name="id849040"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.mean">mean</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
@@ -310,7 +318,7 @@
distribution).
</p>
<a name="math.dist.median"></a><a name="math_toolkit.dist.dist_ref.nmp.median"></a><h5>
<a name="id878077"></a>
<a name="id849194"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.median">median</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
@@ -320,7 +328,7 @@
Returns the median of the distribution <span class="emphasis"><em>dist</em></span>.
</p>
<a name="math.dist.mode"></a><a name="math_toolkit.dist.dist_ref.nmp.mode"></a><h5>
<a name="id878186"></a>
<a name="id849334"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.mode">mode</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
@@ -334,7 +342,7 @@
if the distribution does not have a defined mode.
</p>
<a name="math.dist.pdf"></a><a name="math_toolkit.dist.dist_ref.nmp.probability_density_function"></a><h5>
<a name="id878333"></a>
<a name="id849479"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.probability_density_function">Probability
Density Function</a>
</h5>
@@ -363,7 +371,7 @@
<span class="inlinemediaobject"><img src="../../../../graphs/pdf.png" alt="pdf"></span>
</p>
<a name="math.dist.range"></a><a name="math_toolkit.dist.dist_ref.nmp.range"></a><h5>
<a name="id878502"></a>
<a name="id849694"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.range">range</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
@@ -373,7 +381,7 @@
Returns the valid range of the random variable over distribution <span class="emphasis"><em>dist</em></span>.
</p>
<a name="math.dist.quantile"></a><a name="math_toolkit.dist.dist_ref.nmp.quantile"></a><h5>
<a name="id878638"></a>
<a name="id849867"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.quantile">Quantile</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
@@ -402,7 +410,7 @@
<span class="inlinemediaobject"><img src="../../../../graphs/quantile.png" alt="quantile"></span>
</p>
<a name="math.dist.quantile_c"></a><a name="math_toolkit.dist.dist_ref.nmp.quantile_from_the_complement_of_the_probability_"></a><h5>
<a name="id878861"></a>
<a name="id850148"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.quantile_from_the_complement_of_the_probability_">Quantile
from the complement of the probability.</a>
</h5>
@@ -448,7 +456,7 @@
<span class="inlinemediaobject"><img src="../../../../graphs/survival_inv.png" alt="survival_inv"></span>
</p>
<a name="math.dist.sd"></a><a name="math_toolkit.dist.dist_ref.nmp.standard_deviation"></a><h5>
<a name="id879202"></a>
<a name="id850569"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.standard_deviation">Standard
Deviation</a>
</h5>
@@ -463,7 +471,7 @@
if the distribution does not have a defined standard deviation.
</p>
<a name="math.dist.support"></a><a name="math_toolkit.dist.dist_ref.nmp.support"></a><h5>
<a name="id879322"></a>
<a name="id850725"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.support">support</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
@@ -480,7 +488,7 @@
where the pdf is zero, and the cdf zero or unity.
</p>
<a name="math.dist.variance"></a><a name="math_toolkit.dist.dist_ref.nmp.variance"></a><h5>
<a name="id879466"></a>
<a name="id850914"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.variance">Variance</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
@@ -494,7 +502,7 @@
if the distribution does not have a defined variance.
</p>
<a name="math.dist.skewness"></a><a name="math_toolkit.dist.dist_ref.nmp.skewness"></a><h5>
<a name="id879585"></a>
<a name="id851067"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.skewness">Skewness</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
@@ -508,7 +516,7 @@
if the distribution does not have a defined skewness.
</p>
<a name="math.dist.kurtosis"></a><a name="math_toolkit.dist.dist_ref.nmp.kurtosis"></a><h5>
<a name="id879703"></a>
<a name="id851221"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.kurtosis">Kurtosis</a>
</h5>
<pre class="programlisting"><span class="keyword">template</span> <span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">RealType</span><span class="special">,</span> <span class="keyword">class</span> <a class="link" href="../../policy.html" title="Policies">Policy</a><span class="special">&gt;</span>
@@ -550,7 +558,7 @@
'Proper' kurtosis can have a value from zero to + infinity.
</p>
<a name="math.dist.kurtosis_excess"></a><a name="math_toolkit.dist.dist_ref.nmp.kurtosis_excess"></a><h5>
<a name="id879911"></a>
<a name="id851484"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.kurtosis_excess">Kurtosis
excess</a>
</h5>
@@ -585,7 +593,7 @@
The kurtosis excess of a normal distribution is zero.
</p>
<a name="cdfPQ"></a><a name="math_toolkit.dist.dist_ref.nmp.p_and_q"></a><h5>
<a name="id880096"></a>
<a name="id851716"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.p_and_q">P and Q</a>
</h5>
<p>
@@ -595,7 +603,7 @@
returned by these functions.
</p>
<a name="percent"></a><a name="math_toolkit.dist.dist_ref.nmp.percent_point_function"></a><h5>
<a name="id880126"></a>
<a name="id851762"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.percent_point_function">Percent
Point Function</a>
</h5>
@@ -604,7 +612,7 @@
the <a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
</p>
<a name="cdf_inv"></a><a name="math_toolkit.dist.dist_ref.nmp.inverse_cdf_function_"></a><h5>
<a name="id880151"></a>
<a name="id851803"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.inverse_cdf_function_">Inverse
CDF Function.</a>
</h5>
@@ -613,7 +621,7 @@
<a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
</p>
<a name="survival_inv"></a><a name="math_toolkit.dist.dist_ref.nmp.inverse_survival_function_"></a><h5>
<a name="id880179"></a>
<a name="id851843"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.inverse_survival_function_">Inverse
Survival Function.</a>
</h5>
@@ -621,7 +629,7 @@
The inverse of the survival function, is the same as computing the <a class="link" href="nmp.html#math.dist.quantile_c">quantile from the complement of the probability</a>.
</p>
<a name="pmf"></a><a name="math_toolkit.dist.dist_ref.nmp.probability_mass_function"></a><h5>
<a name="id880209"></a>
<a name="id851884"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.probability_mass_function">Probability
Mass Function</a>
</h5>
@@ -635,7 +643,7 @@
applies to continuous distributions.
</p>
<a name="lower_critical"></a><a name="math_toolkit.dist.dist_ref.nmp.lower_critical_value_"></a><h5>
<a name="id880247"></a>
<a name="id851936"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.lower_critical_value_">Lower
Critical Value.</a>
</h5>
@@ -645,7 +653,7 @@
the <a class="link" href="nmp.html#math.dist.quantile">Quantile</a>.
</p>
<a name="upper_critical"></a><a name="math_toolkit.dist.dist_ref.nmp.upper_critical_value_"></a><h5>
<a name="id880272"></a>
<a name="id851977"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.upper_critical_value_">Upper
Critical Value.</a>
</h5>
@@ -656,7 +664,7 @@
complement of the probability</a>.
</p>
<a name="survival"></a><a name="math_toolkit.dist.dist_ref.nmp.survival_function"></a><h5>
<a name="id880299"></a>
<a name="id852019"></a>
<a class="link" href="nmp.html#math_toolkit.dist.dist_ref.nmp.survival_function">Survival
Function</a>
</h5>
@@ -677,7 +685,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../dist_ref.html"><img src="../../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.html"><img src="../../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="dists.html"><img src="../../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="../dist_ref.html"><img src="../../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist_ref.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="dists.html"><img src="../../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Extras/Future Directions</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../dist.html" title="Statistical Distributions and Functions">
<link rel="prev" href="dist_ref/dist_algorithms.html" title="Distribution Algorithms">
@@ -20,14 +20,14 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="dist_ref/dist_algorithms.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../special.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="dist_ref/dist_algorithms.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.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="../special.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.dist.future"></a><a class="link" href="future.html" title="Extras/Future Directions"> Extras/Future Directions</a>
</h3></div></div></div>
<a name="math_toolkit.dist.future.adding_additional_location_and_scale_parameters"></a><h5>
<a name="id937683"></a>
<a name="id901682"></a>
<a class="link" href="future.html#math_toolkit.dist.future.adding_additional_location_and_scale_parameters">Adding
Additional Location and Scale Parameters</a>
</h5>
@@ -55,7 +55,7 @@
functions.
</p>
<a name="math_toolkit.dist.future.an__quot_any_distribution_quot__class"></a><h5>
<a name="id937847"></a>
<a name="id901887"></a>
<a class="link" href="future.html#math_toolkit.dist.future.an__quot_any_distribution_quot__class">An
"any_distribution" class</a>
</h5>
@@ -84,7 +84,7 @@
use case: this needs more investigation.
</p>
<a name="math_toolkit.dist.future.higher_level_hypothesis_tests"></a><h5>
<a name="id939154"></a>
<a name="id902150"></a>
<a class="link" href="future.html#math_toolkit.dist.future.higher_level_hypothesis_tests">Higher
Level Hypothesis Tests</a>
</h5>
@@ -104,7 +104,7 @@
<span class="emphasis"><em>expected_mean</em></span>.
</p>
<a name="math_toolkit.dist.future.integration_with_statistical_accumulators"></a><h5>
<a name="id939316"></a>
<a name="id902353"></a>
<a class="link" href="future.html#math_toolkit.dist.future.integration_with_statistical_accumulators">Integration
With Statistical Accumulators</a>
</h5>
@@ -136,7 +136,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="dist_ref/dist_algorithms.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="../special.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="dist_ref/dist_algorithms.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.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="../special.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

View File

@@ -2,8 +2,8 @@
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Statistical Distributions Tutorial</title>
<link rel="stylesheet" href="../../../../../../../doc/html/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.74.0">
<link rel="stylesheet" href="../../../../../../../doc/src/boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../index.html" title="Math Toolkit">
<link rel="up" href="../dist.html" title="Statistical Distributions and Functions">
<link rel="prev" href="../dist.html" title="Statistical Distributions and Functions">
@@ -20,9 +20,9 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../dist.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="stat_tut/overview.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="../dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.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="stat_tut/overview.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section" lang="en">
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.dist.stat_tut"></a><a class="link" href="stat_tut.html" title="Statistical Distributions Tutorial"> Statistical Distributions
Tutorial</a>
@@ -148,7 +148,7 @@
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="../dist.html"><img src="../../../../../../../doc/html/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.html"><img src="../../../../../../../doc/html/images/up.png" alt="Up"></a><a accesskey="h" href="../../index.html"><img src="../../../../../../../doc/html/images/home.png" alt="Home"></a><a accesskey="n" href="stat_tut/overview.html"><img src="../../../../../../../doc/html/images/next.png" alt="Next"></a>
<a accesskey="p" href="../dist.html"><img src="../../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../dist.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="stat_tut/overview.html"><img src="../../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>

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