1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Setting the Maximum Interval Halvings and Memory Requirements</title> 5<link rel="stylesheet" href="../../math.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Math Toolkit 2.12.0"> 8<link rel="up" href="../double_exponential.html" title="Double-exponential quadrature"> 9<link rel="prev" href="de_tol.html" title="Setting the Termination Condition for Integration"> 10<link rel="next" href="de_thread.html" title="Thread Safety"> 11</head> 12<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"> 13<table cellpadding="2" width="100%"><tr> 14<td valign="top"><img alt="Boost C++ Libraries" width="277" height="86" src="../../../../../../boost.png"></td> 15<td align="center"><a href="../../../../../../index.html">Home</a></td> 16<td align="center"><a href="../../../../../../libs/libraries.htm">Libraries</a></td> 17<td align="center"><a href="http://www.boost.org/users/people.html">People</a></td> 18<td align="center"><a href="http://www.boost.org/users/faq.html">FAQ</a></td> 19<td align="center"><a href="../../../../../../more/index.htm">More</a></td> 20</tr></table> 21<hr> 22<div class="spirit-nav"> 23<a accesskey="p" href="de_tol.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../double_exponential.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="de_thread.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 24</div> 25<div class="section"> 26<div class="titlepage"><div><div><h3 class="title"> 27<a name="math_toolkit.double_exponential.de_levels"></a><a class="link" href="de_levels.html" title="Setting the Maximum Interval Halvings and Memory Requirements">Setting the 28 Maximum Interval Halvings and Memory Requirements</a> 29</h3></div></div></div> 30<p> 31 The max interval halvings is the maximum number of times the interval can 32 be cut in half before giving up. If the accuracy is not met at that time, 33 the routine returns its best estimate, along with the <code class="computeroutput"><span class="identifier">error</span></code> 34 and <code class="computeroutput"><span class="identifier">L1</span></code>, which allows the 35 user to decide if another quadrature routine should be employed. 36 </p> 37<p> 38 An example of this is 39 </p> 40<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">tol</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special"><</span><span class="keyword">double</span><span class="special">>::</span><span class="identifier">epsilon</span><span class="special">());</span> 41<span class="identifier">size_t</span> <span class="identifier">max_halvings</span> <span class="special">=</span> <span class="number">12</span><span class="special">;</span> 42<span class="identifier">tanh_sinh</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">integrator</span><span class="special">(</span><span class="identifier">max_halvings</span><span class="special">);</span> 43<span class="keyword">auto</span> <span class="identifier">f</span> <span class="special">=</span> <span class="special">[](</span><span class="keyword">double</span> <span class="identifier">x</span><span class="special">)</span> <span class="special">{</span> <span class="keyword">return</span> <span class="number">5</span><span class="special">*</span><span class="identifier">x</span> <span class="special">+</span> <span class="number">7</span><span class="special">;</span> <span class="special">};</span> 44<span class="keyword">double</span> <span class="identifier">error</span><span class="special">,</span> <span class="identifier">L1</span><span class="special">;</span> 45<span class="keyword">double</span> <span class="identifier">Q</span> <span class="special">=</span> <span class="identifier">integrator</span><span class="special">.</span><span class="identifier">integrate</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="special">(</span><span class="keyword">double</span><span class="special">)</span> <span class="number">0</span><span class="special">,</span> <span class="special">(</span><span class="keyword">double</span><span class="special">)</span> <span class="number">1</span><span class="special">,</span> <span class="special">&</span><span class="identifier">error</span><span class="special">,</span> <span class="special">&</span><span class="identifier">L1</span><span class="special">);</span> 46<span class="keyword">if</span> <span class="special">(</span><span class="identifier">error</span><span class="special">*</span><span class="identifier">L1</span> <span class="special">></span> <span class="number">0.01</span><span class="special">)</span> 47<span class="special">{</span> 48 <span class="identifier">Q</span> <span class="special">=</span> <span class="identifier">some_other_quadrature_method</span><span class="special">(</span><span class="identifier">f</span><span class="special">,</span> <span class="special">(</span><span class="keyword">double</span><span class="special">)</span> <span class="number">0</span><span class="special">,</span> <span class="special">(</span><span class="keyword">double</span><span class="special">)</span> <span class="number">1</span><span class="special">);</span> 49<span class="special">}</span> 50</pre> 51<p> 52 It's important to remember that the number of sample points doubles with 53 each new level, as does the memory footprint of the integrator object. Further, 54 if the integral is smooth, then the precision will be doubling with each 55 new level, so that for example, many integrals can achieve 100 decimal digit 56 precision after just 7 levels. That said, abscissa-weight pairs for new levels 57 are computed only when a new level is actually required (see thread safety), 58 none the less, you should avoid setting the maximum arbitrarily high "just 59 in case" as the time and space requirements for a large number of levels 60 can quickly grow out of control. 61 </p> 62</div> 63<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 64<td align="left"></td> 65<td align="right"><div class="copyright-footer">Copyright © 2006-2019 Nikhar 66 Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, 67 Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan 68 Råde, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, 69 Daryle Walker and Xiaogang Zhang<p> 70 Distributed under the Boost Software License, Version 1.0. (See accompanying 71 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>) 72 </p> 73</div></td> 74</tr></table> 75<hr> 76<div class="spirit-nav"> 77<a accesskey="p" href="de_tol.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../double_exponential.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="de_thread.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 78</div> 79</body> 80</html> 81
