1<html> 2<head> 3<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"> 4<title>Eigen Interoperability</title> 5<link rel="stylesheet" href="../../multiprecision.css" type="text/css"> 6<meta name="generator" content="DocBook XSL Stylesheets V1.79.1"> 7<link rel="home" href="../../index.html" title="Chapter 1. Boost.Multiprecision"> 8<link rel="up" href="../tut.html" title="Tutorial"> 9<link rel="prev" href="hash.html" title="Hash Function Support"> 10<link rel="next" href="new_backend.html" title="Writing a New Backend"> 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="hash.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.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="new_backend.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="boost_multiprecision.tut.eigen"></a><a class="link" href="eigen.html" title="Eigen Interoperability">Eigen Interoperability</a> 28</h3></div></div></div> 29<p> 30 This library provides the header: 31 </p> 32<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">eigen</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 33</pre> 34<p> 35 which defines the traits classes and functions that the Eigen library needs 36 all user-defined number types to provide. 37 </p> 38<p> 39 For example the following code performs quad-precision matrix solving on 40 complex numbers: 41 </p> 42<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> 43<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">cpp_complex</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 44<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">multiprecision</span><span class="special">/</span><span class="identifier">eigen</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> 45<span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">Eigen</span><span class="special">/</span><span class="identifier">Dense</span><span class="special">></span> 46 47<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> 48<span class="special">{</span> 49 <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">Eigen</span><span class="special">;</span> 50 <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">multiprecision</span><span class="special">::</span><span class="identifier">cpp_complex_quad</span> <span class="identifier">complex_type</span><span class="special">;</span> 51 <span class="comment">//</span> 52 <span class="comment">// We want to solve Ax = b for x,</span> 53 <span class="comment">// define A and b first:</span> 54 <span class="comment">//</span> 55 <span class="identifier">Matrix</span><span class="special"><</span><span class="identifier">complex_type</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="number">2</span><span class="special">></span> <span class="identifier">A</span><span class="special">,</span> <span class="identifier">b</span><span class="special">;</span> 56 <span class="identifier">A</span> <span class="special"><<</span> <span class="identifier">complex_type</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="number">3</span><span class="special">),</span> <span class="identifier">complex_type</span><span class="special">(-</span><span class="number">1</span><span class="special">,</span> <span class="special">-</span><span class="number">2</span><span class="special">),</span> <span class="identifier">complex_type</span><span class="special">(-</span><span class="number">1</span><span class="special">,</span> <span class="special">-</span><span class="number">4</span><span class="special">),</span> <span class="identifier">complex_type</span><span class="special">(</span><span class="number">3</span><span class="special">,</span> <span class="number">6</span><span class="special">);</span> 57 <span class="identifier">b</span> <span class="special"><<</span> <span class="number">1</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="number">3</span><span class="special">,</span> <span class="number">1</span><span class="special">;</span> 58 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Here is the matrix A:\n"</span> <span class="special"><<</span> <span class="identifier">A</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> 59 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Here is the right hand side b:\n"</span> <span class="special"><<</span> <span class="identifier">b</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> 60 <span class="comment">//</span> 61 <span class="comment">// Solve for x:</span> 62 <span class="comment">//</span> 63 <span class="identifier">Matrix</span><span class="special"><</span><span class="identifier">complex_type</span><span class="special">,</span> <span class="number">2</span><span class="special">,</span> <span class="number">2</span><span class="special">></span> <span class="identifier">x</span> <span class="special">=</span> <span class="identifier">A</span><span class="special">.</span><span class="identifier">fullPivHouseholderQr</span><span class="special">().</span><span class="identifier">solve</span><span class="special">(</span><span class="identifier">b</span><span class="special">);</span> 64 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"The solution is:\n"</span> <span class="special"><<</span> <span class="identifier">x</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> 65 <span class="comment">//</span> 66 <span class="comment">// Compute the error in the solution by using the norms of Ax - b and b:</span> 67 <span class="comment">//</span> 68 <span class="identifier">complex_type</span><span class="special">::</span><span class="identifier">value_type</span> <span class="identifier">relative_error</span> <span class="special">=</span> <span class="special">(</span><span class="identifier">A</span><span class="special">*</span><span class="identifier">x</span> <span class="special">-</span> <span class="identifier">b</span><span class="special">).</span><span class="identifier">norm</span><span class="special">()</span> <span class="special">/</span> <span class="identifier">b</span><span class="special">.</span><span class="identifier">norm</span><span class="special">();</span> 69 <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"The relative error is: "</span> <span class="special"><<</span> <span class="identifier">relative_error</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> 70 <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> 71<span class="special">}</span> 72</pre> 73<p> 74 Which produces the following output: 75 </p> 76<pre class="programlisting"><span class="identifier">Here</span> <span class="identifier">is</span> <span class="identifier">the</span> <span class="identifier">matrix</span> <span class="identifier">A</span><span class="special">:</span> 77<span class="special">(</span><span class="number">2</span><span class="special">,</span><span class="number">3</span><span class="special">)</span> <span class="special">(-</span><span class="number">1</span><span class="special">,-</span><span class="number">2</span><span class="special">)</span> 78<span class="special">(-</span><span class="number">1</span><span class="special">,-</span><span class="number">4</span><span class="special">)</span> <span class="special">(</span><span class="number">3</span><span class="special">,</span><span class="number">6</span><span class="special">)</span> 79<span class="identifier">Here</span> <span class="identifier">is</span> <span class="identifier">the</span> <span class="identifier">right</span> <span class="identifier">hand</span> <span class="identifier">side</span> <span class="identifier">b</span><span class="special">:</span> 80<span class="number">1</span> <span class="number">2</span> 81<span class="number">3</span> <span class="number">1</span> 82<span class="identifier">The</span> <span class="identifier">solution</span> <span class="identifier">is</span><span class="special">:</span> 83<span class="special">(</span><span class="number">0.6</span><span class="special">,-</span><span class="number">0.6</span><span class="special">)</span> <span class="special">(</span><span class="number">0.7</span><span class="special">,-</span><span class="number">0.7</span><span class="special">)</span> 84<span class="special">(</span><span class="number">0.64</span><span class="special">,-</span><span class="number">0.68</span><span class="special">)</span> <span class="special">(</span><span class="number">0.58</span><span class="special">,-</span><span class="number">0.46</span><span class="special">)</span> 85<span class="identifier">The</span> <span class="identifier">relative</span> <span class="identifier">error</span> <span class="identifier">is</span><span class="special">:</span> <span class="number">2.63132e-34</span> 86</pre> 87</div> 88<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> 89<td align="left"></td> 90<td align="right"><div class="copyright-footer">Copyright © 2002-2020 John 91 Maddock and Christopher Kormanyos<p> 92 Distributed under the Boost Software License, Version 1.0. (See accompanying 93 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>) 94 </p> 95</div></td> 96</tr></table> 97<hr> 98<div class="spirit-nav"> 99<a accesskey="p" href="hash.html"><img src="../../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../tut.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="new_backend.html"><img src="../../../../../../doc/src/images/next.png" alt="Next"></a> 100</div> 101</body> 102</html> 103
