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  27 <a name="math_toolkit.vector_barycentric"></a><a class="link" href="vector_barycentric.html" title="Vector-valued Barycentric Rational Interpolation">Vector-valued Barycentric
  28     Rational Interpolation</a>
  29 </h2></div></div></div>
  30 <h4>
  31 <a name="math_toolkit.vector_barycentric.h0"></a>
  32       <span class="phrase"><a name="math_toolkit.vector_barycentric.synopsis"></a></span><a class="link" href="vector_barycentric.html#math_toolkit.vector_barycentric.synopsis">Synopsis</a>
  33     </h4>
  34 <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">math</span><span class="special">/</span><span class="identifier">interpolators</span><span class="special">/</span><span class="identifier">vector_barycentric_rational</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  35
  36 <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">math</span><span class="special">{</span>
  37
  38 <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">class</span> <span class="identifier">TimeContainer</span><span class="special">,</span> <span class="keyword">class</span> <span class="identifier">SpaceContainer</span><span class="special">&gt;</span>
  39 <span class="keyword">class</span> <span class="identifier">vector_barycentric_rational</span>
  40 <span class="special">{</span>
  41 <span class="keyword">public</span><span class="special">:</span>
  42     <span class="keyword">using</span> <span class="identifier">Real</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">TimeContainer</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
  43     <span class="keyword">using</span> <span class="identifier">Point</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">SpaceContainer</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
  44     <span class="identifier">vector_barycentric_rational</span><span class="special">(</span><span class="identifier">TimeContainer</span><span class="special">&amp;&amp;</span> <span class="identifier">times</span><span class="special">,</span> <span class="identifier">SpaceContainer</span><span class="special">&amp;&amp;</span> <span class="identifier">points</span><span class="special">,</span> <span class="identifier">size_t</span> <span class="identifier">approximation_order</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span>
  45
  46     <span class="keyword">void</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Point</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
  47
  48     <span class="identifier">Point</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
  49
  50     <span class="keyword">void</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Point</span><span class="special">&amp;</span> <span class="identifier">dxdt</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
  51
  52     <span class="identifier">Point</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">t</span><span class="special">);</span>
  53
  54     <span class="keyword">void</span> <span class="identifier">eval_with_prime</span><span class="special">(</span><span class="identifier">Point</span><span class="special">&amp;</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Point</span><span class="special">&amp;</span> <span class="identifier">dxdt</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
  55
  56     <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special">&lt;</span><span class="identifier">Point</span><span class="special">,</span> <span class="identifier">Point</span><span class="special">&gt;</span> <span class="identifier">eval_with_prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">t</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
  57 <span class="special">};</span>
  58
  59 <span class="special">}}</span>
  60 </pre>
  61 <h4>
  62 <a name="math_toolkit.vector_barycentric.h1"></a>
  63       <span class="phrase"><a name="math_toolkit.vector_barycentric.description"></a></span><a class="link" href="vector_barycentric.html#math_toolkit.vector_barycentric.description">Description</a>
  64     </h4>
  65 <p>
  66       The <span class="emphasis"><em>n</em></span> dimensional vector-valued barycentric rational interpolator
  67       is exactly the same as <span class="emphasis"><em>n</em></span> scalar-valued barycentric rational
  68       interpolators. This is provided primarily for convenience and a slight improvement
  69       in efficiency over using <span class="emphasis"><em>n</em></span> different rational interpolators
  70       and combining their results.
  71     </p>
  72 <p>
  73       Use of the class requires a <code class="computeroutput"><span class="identifier">Point</span></code>-type
  74       which has size known at compile-time. These requirements are satisfied by (for
  75       example) <code class="computeroutput"><span class="identifier">Eigen</span><span class="special">::</span><span class="identifier">Vector2d</span></code>s and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">array</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">,</span> <span class="identifier">N</span><span class="special">&gt;</span></code> classes. The call to the constructor computes
  76       the weights:
  77     </p>
  78 <pre class="programlisting"><span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">vector_barycentric_rational</span><span class="special">;</span>
  79 <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">t</span><span class="special">(</span><span class="number">100</span><span class="special">);</span>
  80 <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">Eigen</span><span class="special">::</span><span class="identifier">Vector2d</span><span class="special">&gt;</span> <span class="identifier">y</span><span class="special">(</span><span class="number">100</span><span class="special">);</span>
  81 <span class="comment">// initialize t and y . . .</span>
  82 <span class="identifier">vector_barycentric_rational</span><span class="special">&lt;</span><span class="keyword">decltype</span><span class="special">(</span><span class="identifier">t</span><span class="special">),</span> <span class="keyword">decltype</span><span class="special">(</span><span class="identifier">y</span><span class="special">)&gt;</span> <span class="identifier">interpolant</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">t</span><span class="special">),</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">y</span><span class="special">));</span>
  83 </pre>
  84 <p>
  85       To evaluate the interpolant, use
  86     </p>
  87 <pre class="programlisting"><span class="keyword">double</span> <span class="identifier">t</span> <span class="special">=</span> <span class="number">2.3</span><span class="special">;</span>
  88 <span class="identifier">Eigen</span><span class="special">::</span><span class="identifier">Vector2d</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">interpolant</span><span class="special">(</span><span class="identifier">t</span><span class="special">);</span>
  89 </pre>
  90 <p>
  91       If you want to populate a vector passed into the interpolant, rather than get
  92       it returned, that syntax is supported:
  93     </p>
  94 <pre class="programlisting"><span class="identifier">Eigen</span><span class="special">::</span><span class="identifier">Vector2d</span> <span class="identifier">y</span><span class="special">;</span>
  95 <span class="identifier">interpolant</span><span class="special">(</span><span class="identifier">y</span><span class="special">,</span> <span class="identifier">t</span><span class="special">);</span>
  96 </pre>
  97 <p>
  98       We tested this with <code class="computeroutput"><span class="identifier">Eigen</span><span class="special">::</span><span class="identifier">Vector</span></code>s and found no performance benefit,
  99       but other <code class="computeroutput"><span class="identifier">Point</span></code>-types might
 100       not be the same.
 101     </p>
 102 <p>
 103       To evaluate the derivative of the interpolant use
 104     </p>
 105 <pre class="programlisting"><span class="keyword">auto</span> <span class="special">[</span><span class="identifier">y</span><span class="special">,</span> <span class="identifier">y_prime</span><span class="special">]</span> <span class="special">=</span> <span class="identifier">interpolant</span><span class="special">.</span><span class="identifier">eval_with_prime</span><span class="special">(</span><span class="identifier">x</span><span class="special">);</span>
 106 </pre>
 107 <p>
 108       Computation of the derivative requires evaluation, so if you can try to use
 109       both values at once.
 110     </p>
 111 </div>
 112 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 113 <td align="left"></td>
 114 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
 115       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
 116       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
 117       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
 118       Daryle Walker and Xiaogang Zhang<p>
 119         Distributed under the Boost Software License, Version 1.0. (See accompanying
 120         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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