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  26 <div class="titlepage"><div><div><h2 class="title" style="clear: both">
  27 <a name="math_toolkit.cardinal_quadratic_b"></a><a class="link" href="cardinal_quadratic_b.html" title="Cardinal Quadratic B-spline interpolation">Cardinal Quadratic B-spline
  28     interpolation</a>
  29 </h2></div></div></div>
  30 <h4>
  31 <a name="math_toolkit.cardinal_quadratic_b.h0"></a>
  32       <span class="phrase"><a name="math_toolkit.cardinal_quadratic_b.synopsis"></a></span><a class="link" href="cardinal_quadratic_b.html#math_toolkit.cardinal_quadratic_b.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">cardinal_quadratic_b_spline</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
  35 </pre>
  36 <pre class="programlisting"><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> <span class="keyword">namespace</span> <span class="identifier">interpolators</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">Real</span><span class="special">&gt;</span>
  39 <span class="keyword">class</span> <span class="identifier">cardinal_quadratic_b_spline</span>
  40 <span class="special">{</span>
  41 <span class="keyword">public</span><span class="special">:</span>
  42     <span class="comment">// If you don't know the value of the derivative at the endpoints, leave them as NaNs and the routine will estimate them.</span>
  43     <span class="comment">// y[0] = y(a), y[n - 1] = y(b), step_size = (b - a)/(n -1).</span>
  44     <span class="identifier">cardinal_quadratic_b_spline</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">Real</span><span class="special">*</span> <span class="keyword">const</span> <span class="identifier">y</span><span class="special">,</span>
  45                                 <span class="identifier">size_t</span> <span class="identifier">n</span><span class="special">,</span>
  46                                 <span class="identifier">Real</span> <span class="identifier">t0</span> <span class="comment">/* initial time, left endpoint */</span><span class="special">,</span>
  47                                 <span class="identifier">Real</span> <span class="identifier">h</span>  <span class="comment">/*spacing, stepsize*/</span><span class="special">,</span>
  48                                 <span class="identifier">Real</span> <span class="identifier">left_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">(),</span>
  49                                 <span class="identifier">Real</span> <span class="identifier">right_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">())</span>
  50
  51     <span class="identifier">cardinal_quadratic_b_spline</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;</span> <span class="keyword">const</span> <span class="special">&amp;</span> <span class="identifier">y</span><span class="special">,</span>
  52                                 <span class="identifier">Real</span> <span class="identifier">t0</span> <span class="comment">/* initial time, left endpoint */</span><span class="special">,</span>
  53                                 <span class="identifier">Real</span> <span class="identifier">h</span>  <span class="comment">/*spacing, stepsize*/</span><span class="special">,</span>
  54                                 <span class="identifier">Real</span> <span class="identifier">left_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">(),</span>
  55                                 <span class="identifier">Real</span> <span class="identifier">right_endpoint_derivative</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">numeric_limits</span><span class="special">&lt;</span><span class="identifier">Real</span><span class="special">&gt;::</span><span class="identifier">quiet_NaN</span><span class="special">())</span>
  56
  57     <span class="identifier">Real</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>
  58
  59     <span class="identifier">Real</span> <span class="identifier">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>
  60 <span class="special">};</span>
  61 <span class="special">}}}</span>
  62 </pre>
  63 <h4>
  64 <a name="math_toolkit.cardinal_quadratic_b.h1"></a>
  65       <span class="phrase"><a name="math_toolkit.cardinal_quadratic_b.cardinal_quadratic_b_spline_inte"></a></span><a class="link" href="cardinal_quadratic_b.html#math_toolkit.cardinal_quadratic_b.cardinal_quadratic_b_spline_inte">Cardinal
  66       Quadratic B-Spline Interpolation</a>
  67     </h4>
  68 <p>
  69       The cardinal quadratic B-spline interpolator is very nearly the same as the
  70       cubic B-spline interpolator, with the modification that the basis functions
  71       are constructed by convolving a box function with itself twice, rather than
  72       three times as is done with the cubic B-spline.
  73     </p>
  74 <p>
  75       Since the basis functions are less smooth than the cubic B-spline, you will
  76       nearly always wish to use the cubic B-spline interpolator rather than this.
  77       However, this interpolator is occasionally useful for approximating functions
  78       of reduced smoothness, as hence finds use internally in the Boost.Math library.
  79     </p>
  80 <p>
  81       It is reasonable to test this interpolator against the cubic b-spline interpolator
  82       when you are approximating functions which are two or three times continuously
  83       differentiable, but not three or four times differentiable.
  84     </p>
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  88 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2019 Nikhar
  89       Agrawal, Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos,
  90       Hubert Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Matthew Pulver, Johan
  91       R&#229;de, Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg,
  92       Daryle Walker and Xiaogang Zhang<p>
  93         Distributed under the Boost Software License, Version 1.0. (See accompanying
  94         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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