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    25. 

  25. <div class="section">
    26. 

  26. <div class="titlepage"><div><div><h3 class="title">
    27. 

  27. <a name="boost_multiprecision.tut.eigen"></a><a class="link" href="eigen.html" title="Eigen Interoperability">Eigen Interoperability</a>
    28. 

  28. </h3></div></div></div>
    29. 

  29. <p>
    30. 

  30.         This library provides the header:
    31. 

  31.       </p>
    32. 

  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. 

  33. </pre>
    34. 

  34. <p>
    35. 

  35.         which defines the traits classes and functions that the Eigen library needs
    36. 

  36.         all user-defined number types to provide.
    37. 

  37.       </p>
    38. 

  38. <p>
    39. 

  39.         For example the following code performs quad-precision matrix solving on
    40. 

  40.         complex numbers:
    41. 

  41.       </p>
    42. 

  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. 

  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. 

  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. 

  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. 

  46. 

  47. <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
    48. 

  48. <span class="special">{</span>
    49. 

  49.    <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">Eigen</span><span class="special">;</span>
    50. 

  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. 

  51.    <span class="comment">//</span>
    52. 

  52.    <span class="comment">// We want to solve Ax = b for x,</span>
    53. 

  53.    <span class="comment">// define A and b first:</span>
    54. 

  54.    <span class="comment">//</span>
    55. 

  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. 

  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. 

  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. 

  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. 

  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. 

  60.    <span class="comment">//</span>
    61. 

  61.    <span class="comment">// Solve for x:</span>
    62. 

  62.    <span class="comment">//</span>
    63. 

  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. 

  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. 

  65.    <span class="comment">//</span>
    66. 

  66.    <span class="comment">// Compute the error in the solution by using the norms of Ax - b and b:</span>
    67. 

  67.    <span class="comment">//</span>
    68. 

  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. 

  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. 

  70.    <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
    71. 

  71. <span class="special">}</span>
    72. 

  72. </pre>
    73. 

  73. <p>
    74. 

  74.         Which produces the following output:
    75. 

  75.       </p>
    76. 

  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. 

  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. 

  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. 

  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. 

  80. <span class="number">1</span> <span class="number">2</span>
    81. 

  81. <span class="number">3</span> <span class="number">1</span>
    82. 

  82. <span class="identifier">The</span> <span class="identifier">solution</span> <span class="identifier">is</span><span class="special">:</span>
    83. 

  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. 

  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. 

  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. 

  86. </pre>
    87. 

  87. </div>
    88. 

  88. <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
    89. 

  89. <td align="left"></td>
    90. 

  90. <td align="right"><div class="copyright-footer">Copyright &#169; 2002-2019 John Maddock
    91. 

  91.       and Christopher Kormanyos<p>
    92. 

  92.         Distributed under the Boost Software License, Version 1.0. (See accompanying
    93. 

  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. 

  94.       </p>
    95. 

  95. </div></td>
    96. 

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    97. 

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