townforge/math
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity
cc
math/doc/html/math_toolkit/root_finding_examples/lambda.html
jzmaddock 72e469da0a Update version number in docs. 
[CI SKIP]
2019-10-31 17:55:35 +00:00

80 lines
9.3 KiB
HTML
Raw Permalink Blame History

<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>Using C++11 Lambda's</title>
<link rel="stylesheet" href="../../math.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.79.1">
<link rel="home" href="../../index.html" title="Math Toolkit 2.11.0">
<link rel="up" href="../root_finding_examples.html" title="Examples of Root-Finding (with and without derivatives)">
<link rel="prev" href="cbrt_eg.html" title="Finding the Cubed Root With and Without Derivatives">
<link rel="next" href="5th_root_eg.html" title="Computing the Fifth Root">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr>
<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td>
<td align="center"><a href="../../../../../../index.html">Home</a></td>
<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td>
<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td>
<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td>
<td align="center"><a href="../../../../../../more/index.htm">More</a></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="cbrt_eg.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../root_finding_examples.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="5th_root_eg.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.root_finding_examples.lambda"></a><a class="link" href="lambda.html" title="Using C++11 Lambda's">Using C++11
Lambda's</a>
</h3></div></div></div>
<p>
Since all the root finding functions accept a function-object, they can be
made to work (often in a lot less code) with C++11 lambda's. Here's the much
reduced code for our "toy" cube root function:
</p>
<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">T</span> <span class="identifier">cbrt_2deriv_lambda</span><span class="special">(</span><span class="identifier">T</span> <span class="identifier">x</span><span class="special">)</span>
<span class="special">{</span>
<span class="comment">// return cube root of x using 1st and 2nd derivatives and Halley.</span>
<span class="comment">//using namespace std; // Help ADL of std functions.</span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">tools</span><span class="special">;</span>
<span class="keyword">int</span> <span class="identifier">exponent</span><span class="special">;</span>
<span class="identifier">frexp</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="special">&amp;</span><span class="identifier">exponent</span><span class="special">);</span> <span class="comment">// Get exponent of z (ignore mantissa).</span>
<span class="identifier">T</span> <span class="identifier">guess</span> <span class="special">=</span> <span class="identifier">ldexp</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">exponent</span> <span class="special">/</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// Rough guess is to divide the exponent by three.</span>
<span class="identifier">T</span> <span class="identifier">min</span> <span class="special">=</span> <span class="identifier">ldexp</span><span class="special">(</span><span class="number">0.5</span><span class="special">,</span> <span class="identifier">exponent</span> <span class="special">/</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// Minimum possible value is half our guess.</span>
<span class="identifier">T</span> <span class="identifier">max</span> <span class="special">=</span> <span class="identifier">ldexp</span><span class="special">(</span><span class="number">2.</span><span class="special">,</span> <span class="identifier">exponent</span> <span class="special">/</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// Maximum possible value is twice our guess.</span>
<span class="keyword">const</span> <span class="keyword">int</span> <span class="identifier">digits</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">T</span><span class="special">&gt;::</span><span class="identifier">digits</span><span class="special">;</span> <span class="comment">// Maximum possible binary digits accuracy for type T.</span>
<span class="comment">// digits used to control how accurate to try to make the result.</span>
<span class="keyword">int</span> <span class="identifier">get_digits</span> <span class="special">=</span> <span class="keyword">static_cast</span><span class="special">&lt;</span><span class="keyword">int</span><span class="special">&gt;(</span><span class="identifier">digits</span> <span class="special">*</span> <span class="number">0.4</span><span class="special">);</span> <span class="comment">// Accuracy triples with each step, so stop when just</span>
<span class="comment">// over one third of the digits are correct.</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span> <span class="identifier">maxit</span> <span class="special">=</span> <span class="number">20</span><span class="special">;</span>
<span class="identifier">T</span> <span class="identifier">result</span> <span class="special">=</span> <span class="identifier">halley_iterate</span><span class="special">(</span>
<span class="comment">// lambda function:</span>
<span class="special">[</span><span class="identifier">x</span><span class="special">](</span><span class="keyword">const</span> <span class="identifier">T</span><span class="special">&amp;</span> <span class="identifier">g</span><span class="special">){</span> <span class="keyword">return</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">make_tuple</span><span class="special">(</span><span class="identifier">g</span> <span class="special">*</span> <span class="identifier">g</span> <span class="special">*</span> <span class="identifier">g</span> <span class="special">-</span> <span class="identifier">x</span><span class="special">,</span> <span class="number">3</span> <span class="special">*</span> <span class="identifier">g</span> <span class="special">*</span> <span class="identifier">g</span><span class="special">,</span> <span class="number">6</span> <span class="special">*</span> <span class="identifier">g</span><span class="special">);</span> <span class="special">},</span>
<span class="identifier">guess</span><span class="special">,</span> <span class="identifier">min</span><span class="special">,</span> <span class="identifier">max</span><span class="special">,</span> <span class="identifier">get_digits</span><span class="special">,</span> <span class="identifier">maxit</span><span class="special">);</span>
<span class="keyword">return</span> <span class="identifier">result</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
Full code of this example is at <a href="../../../../example/root_finding_example.cpp" target="_top">root_finding_example.cpp</a>,
</p>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
Daryle Walker and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="cbrt_eg.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../root_finding_examples.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="5th_root_eg.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a>
</div>
</body>
</html>
Reference in New Issue View Git Blame Copy Permalink