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  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">&lt;</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">&gt;</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">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>
  43 <span class="preprocessor">#include</span> <span class="special">&lt;</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">&gt;</span>
  44 <span class="preprocessor">#include</span> <span class="special">&lt;</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">&gt;</span>
  45 <span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">Eigen</span><span class="special">/</span><span class="identifier">Dense</span><span class="special">&gt;</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">&lt;</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">&gt;</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">&lt;&lt;</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">&lt;&lt;</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">&lt;&lt;</span> <span class="string">"Here is the matrix A:\n"</span> <span class="special">&lt;&lt;</span> <span class="identifier">A</span> <span class="special">&lt;&lt;</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">&lt;&lt;</span> <span class="string">"Here is the right hand side b:\n"</span> <span class="special">&lt;&lt;</span> <span class="identifier">b</span> <span class="special">&lt;&lt;</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">&lt;</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">&gt;</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">&lt;&lt;</span> <span class="string">"The solution is:\n"</span> <span class="special">&lt;&lt;</span> <span class="identifier">x</span> <span class="special">&lt;&lt;</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">&lt;&lt;</span> <span class="string">"The relative error is: "</span> <span class="special">&lt;&lt;</span> <span class="identifier">relative_error</span> <span class="special">&lt;&lt;</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>
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  89 <td align="left"></td>
  90 <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2019 John Maddock
  91       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>)
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