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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
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<a name="math_toolkit.quintic_hermite"></a><a class="link" href="quintic_hermite.html" title="Quintic Hermite interpolation">Quintic Hermite interpolation</a>
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</h2></div></div></div>
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<h4>
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<a name="math_toolkit.quintic_hermite.h0"></a>
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<span class="phrase"><a name="math_toolkit.quintic_hermite.synopsis"></a></span><a class="link" href="quintic_hermite.html#math_toolkit.quintic_hermite.synopsis">Synopsis</a>
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</h4>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</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">quintic_hermite</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<span class="keyword">namespace</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>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">RandomAccessContainer</span><span class="special">></span>
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<span class="keyword">class</span> <span class="identifier">quintic_hermite</span> <span class="special">{</span>
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<span class="keyword">public</span><span class="special">:</span>
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<span class="keyword">using</span> <span class="identifier">Real</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">RandomAccessContainer</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
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<span class="identifier">quintic_hermite</span><span class="special">(</span><span class="identifier">RandomAccessContainer</span> <span class="special">&&</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">RandomAccessContainer</span> <span class="special">&&</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">RandomAccessContainer</span> <span class="special">&&</span> <span class="identifier">dydx</span><span class="special">,</span> <span class="identifier">RandomAccessContainer</span> <span class="special">&&</span> <span class="identifier">d2ydx2</span><span class="special">)</span>
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<span class="keyword">inline</span> <span class="identifier">Real</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="keyword">inline</span> <span class="identifier">Real</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="keyword">inline</span> <span class="identifier">Real</span> <span class="identifier">double_prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">Real</span><span class="special">,</span> <span class="identifier">Real</span><span class="special">></span> <span class="identifier">domain</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="keyword">friend</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span><span class="special">&</span> <span class="keyword">operator</span><span class="special"><<(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream</span> <span class="special">&</span> <span class="identifier">os</span><span class="special">,</span> <span class="keyword">const</span> <span class="identifier">quintic_hermite</span> <span class="special">&</span> <span class="identifier">m</span><span class="special">);</span>
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<span class="keyword">void</span> <span class="identifier">push_back</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">dydx</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">d2ydx2</span><span class="special">);</span>
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<span class="special">};</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">RandomAccessContainer</span><span class="special">></span>
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<span class="keyword">class</span> <span class="identifier">cardinal_quintic_hermite</span> <span class="special">{</span>
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<span class="keyword">public</span><span class="special">:</span>
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<span class="keyword">using</span> <span class="identifier">Real</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">RandomAccessContainer</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
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<span class="identifier">cardinal_quintic_hermite</span><span class="special">(</span><span class="identifier">RandomAccessContainer</span> <span class="special">&&</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">RandomAccessContainer</span> <span class="special">&&</span> <span class="identifier">dydx</span><span class="special">,</span> <span class="identifier">RandomAccessContainer</span> <span class="special">&&</span> <span class="identifier">d2ydx2</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">x0</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">dx</span><span class="special">);</span>
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<span class="keyword">inline</span> <span class="identifier">Real</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="keyword">inline</span> <span class="identifier">Real</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="keyword">inline</span> <span class="identifier">Real</span> <span class="identifier">double_prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">Real</span><span class="special">,</span> <span class="identifier">Real</span><span class="special">></span> <span class="identifier">domain</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="special">};</span>
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<span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span> <span class="identifier">RandomAccessContainer</span><span class="special">></span>
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<span class="keyword">class</span> <span class="identifier">cardinal_quintic_hermite_aos</span> <span class="special">{</span>
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<span class="keyword">public</span><span class="special">:</span>
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<span class="keyword">using</span> <span class="identifier">Point</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">RandomAccessContainer</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
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<span class="keyword">using</span> <span class="identifier">Real</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">Point</span><span class="special">::</span><span class="identifier">value_type</span><span class="special">;</span>
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<span class="identifier">cardinal_quintic_hermite_aos</span><span class="special">(</span><span class="identifier">RandomAccessContainer</span> <span class="special">&&</span> <span class="identifier">data</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">x0</span><span class="special">,</span> <span class="identifier">Real</span> <span class="identifier">dx</span><span class="special">)</span>
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<span class="keyword">inline</span> <span class="identifier">Real</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="keyword">inline</span> <span class="identifier">Real</span> <span class="identifier">prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="keyword">inline</span> <span class="identifier">Real</span> <span class="identifier">double_prime</span><span class="special">(</span><span class="identifier">Real</span> <span class="identifier">x</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="identifier">Real</span><span class="special">,</span> <span class="identifier">Real</span><span class="special">></span> <span class="identifier">domain</span><span class="special">()</span> <span class="keyword">const</span><span class="special">;</span>
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<span class="special">}</span>
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</pre>
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<h4>
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<a name="math_toolkit.quintic_hermite.h1"></a>
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<span class="phrase"><a name="math_toolkit.quintic_hermite.quintic_hermite_interpolation"></a></span><a class="link" href="quintic_hermite.html#math_toolkit.quintic_hermite.quintic_hermite_interpolation">Quintic
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Hermite Interpolation</a>
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</h4>
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<p>
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The quintic Hermite interpolator takes a list of possibly non-uniformly spaced
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abscissas, ordinates, and their velocities and accelerations which are used
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to construct a quintic interpolating polynomial between segments. This is useful
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for taking solution skeletons from ODE steppers and turning them into a continuous
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function, provided that the right-hand side <span class="emphasis"><em>f</em></span>(<span class="emphasis"><em>x</em></span>,
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<span class="emphasis"><em>y</em></span>) is differentiable along the solution path. The interpolant
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is <span class="emphasis"><em>C</em></span><sup>2</sup> and its evaluation has 𝑶(log(<span class="emphasis"><em>N</em></span>))
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complexity. An example usage is as follows:
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</p>
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<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">x</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">4</span><span class="special">,</span> <span class="number">5</span><span class="special">,</span> <span class="number">6</span><span class="special">};</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">y</span><span class="special">{</span><span class="number">7</span><span class="special">,</span><span class="number">8</span><span class="special">,</span><span class="number">9</span><span class="special">,</span><span class="number">10</span><span class="special">,</span><span class="number">11</span><span class="special">,</span><span class="number">12</span><span class="special">};</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">dydx</span><span class="special">{</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">};</span>
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<span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">d2ydx2</span><span class="special">{</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">};</span>
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<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">interpolators</span><span class="special">::</span><span class="identifier">quintic_hermite</span><span class="special">;</span>
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<span class="keyword">auto</span> <span class="identifier">spline</span> <span class="special">=</span> <span class="identifier">quintic_hermite</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">x</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> <span class="identifier">std</span><span class="special">::</span><span class="identifier">move</span><span class="special">(</span><span class="identifier">dydx</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">d2ydx2</span><span class="special">));</span>
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<span class="comment">// evaluate at a point:</span>
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<span class="keyword">double</span> <span class="identifier">z</span> <span class="special">=</span> <span class="identifier">spline</span><span class="special">(</span><span class="number">3.4</span><span class="special">);</span>
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<span class="comment">// evaluate derivative at a point:</span>
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<span class="keyword">double</span> <span class="identifier">zprime</span> <span class="special">=</span> <span class="identifier">spline</span><span class="special">.</span><span class="identifier">prime</span><span class="special">(</span><span class="number">3.4</span><span class="special">);</span>
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</pre>
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<p>
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Periodically, it is helpful to see what data the interpolator has. This can
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be achieved via
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</p>
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<pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">spline</span> <span class="special"><<</span> <span class="string">"\n"</span><span class="special">;</span>
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</pre>
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<p>
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Note that the interpolator is pimpl'd, so that copying the class is cheap,
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and hence it can be shared between threads. (The call operator and <code class="computeroutput"><span class="special">.</span><span class="identifier">prime</span><span class="special">()</span></code>
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are threadsafe.)
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</p>
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<p>
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The interpolator can be updated in constant time. Hence we can use <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">circular_buffer</span></code>
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to do real-time interpolation.
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</p>
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<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">circular_buffer</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
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<span class="special">...</span>
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<span class="identifier">boost</span><span class="special">::</span><span class="identifier">circular_buffer</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">initial_x</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">4</span><span class="special">};</span>
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<span class="identifier">boost</span><span class="special">::</span><span class="identifier">circular_buffer</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">initial_y</span><span class="special">{</span><span class="number">4</span><span class="special">,</span><span class="number">5</span><span class="special">,</span><span class="number">6</span><span class="special">,</span><span class="number">7</span><span class="special">};</span>
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<span class="identifier">boost</span><span class="special">::</span><span class="identifier">circular_buffer</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">initial_dydx</span><span class="special">{</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">,</span><span class="number">1</span><span class="special">};</span>
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<span class="identifier">boost</span><span class="special">::</span><span class="identifier">circular_buffer</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">initial_d2ydx2</span><span class="special">{</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">,</span><span class="number">0</span><span class="special">};</span>
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<span class="keyword">auto</span> <span class="identifier">circular_akima</span> <span class="special">=</span> <span class="identifier">quintic_hermite</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">initial_x</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">initial_y</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">initial_dydx</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">initial_d2ydx2</span><span class="special">));</span>
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<span class="comment">// interpolate via call operation:</span>
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||
<span class="keyword">double</span> <span class="identifier">y</span> <span class="special">=</span> <span class="identifier">circular_akima</span><span class="special">(</span><span class="number">3.5</span><span class="special">);</span>
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<span class="comment">// add new data:</span>
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<span class="identifier">circular_akima</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="number">8</span><span class="special">,</span> <span class="number">1</span><span class="special">,</span> <span class="number">0</span><span class="special">);</span>
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<span class="comment">// interpolate at 4.5:</span>
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||
<span class="identifier">y</span> <span class="special">=</span> <span class="identifier">circular_akima</span><span class="special">(</span><span class="number">4.5</span><span class="special">);</span>
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</pre>
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<p>
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<span class="inlinemediaobject"><object type="image/svg+xml" data="../../graphs/quintic_sine_approximation.svg"></object></span>
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</p>
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<p>
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For equispaced data, we can use <code class="computeroutput"><span class="identifier">cardinal_quintic_hermite</span></code>
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or <code class="computeroutput"><span class="identifier">cardinal_quintic_hermite_aos</span></code>
|
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to get constant-time evaluation. This is useful in memory-constrained or performance
|
||
critical applications where data is equispaced.
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||
</p>
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<h4>
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||
<a name="math_toolkit.quintic_hermite.h2"></a>
|
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<span class="phrase"><a name="math_toolkit.quintic_hermite.complexity_and_performance"></a></span><a class="link" href="quintic_hermite.html#math_toolkit.quintic_hermite.complexity_and_performance">Complexity
|
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and Performance</a>
|
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</h4>
|
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<p>
|
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The following google benchmark demonstrates the cost of the call operator for
|
||
this interpolator:
|
||
</p>
|
||
<pre class="programlisting"><span class="identifier">Run</span> <span class="identifier">on</span> <span class="special">(</span><span class="number">16</span> <span class="identifier">X</span> <span class="number">4300</span> <span class="identifier">MHz</span> <span class="identifier">CPU</span> <span class="identifier">s</span><span class="special">)</span>
|
||
<span class="identifier">CPU</span> <span class="identifier">Caches</span><span class="special">:</span>
|
||
<span class="identifier">L1</span> <span class="identifier">Data</span> <span class="number">32</span><span class="identifier">K</span> <span class="special">(</span><span class="identifier">x8</span><span class="special">)</span>
|
||
<span class="identifier">L1</span> <span class="identifier">Instruction</span> <span class="number">32</span><span class="identifier">K</span> <span class="special">(</span><span class="identifier">x8</span><span class="special">)</span>
|
||
<span class="identifier">L2</span> <span class="identifier">Unified</span> <span class="number">1024</span><span class="identifier">K</span> <span class="special">(</span><span class="identifier">x8</span><span class="special">)</span>
|
||
<span class="identifier">L3</span> <span class="identifier">Unified</span> <span class="number">11264</span><span class="identifier">K</span> <span class="special">(</span><span class="identifier">x1</span><span class="special">)</span>
|
||
<span class="identifier">Load</span> <span class="identifier">Average</span><span class="special">:</span> <span class="number">0.92</span><span class="special">,</span> <span class="number">0.64</span><span class="special">,</span> <span class="number">0.35</span>
|
||
<span class="special">--------------------------------------------------</span>
|
||
<span class="identifier">Benchmark</span> <span class="identifier">Time</span>
|
||
<span class="special">--------------------------------------------------</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">8</span> <span class="number">8.14</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">16</span> <span class="number">8.69</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">32</span> <span class="number">9.42</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">64</span> <span class="number">9.90</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">128</span> <span class="number">10.4</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">256</span> <span class="number">10.9</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">512</span> <span class="number">11.6</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">1024</span> <span class="number">12.3</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">2048</span> <span class="number">12.8</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">4096</span> <span class="number">13.6</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">8192</span> <span class="number">14.6</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">16384</span> <span class="number">15.5</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">32768</span> <span class="number">17.4</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">65536</span> <span class="number">18.5</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">131072</span> <span class="number">18.8</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">262144</span> <span class="number">19.8</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">524288</span> <span class="number">20.5</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">1048576</span> <span class="number">21.6</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">2097152</span> <span class="number">22.5</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">4194304</span> <span class="number">24.2</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">8388608</span> <span class="number">26.6</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">16777216</span> <span class="number">26.7</span> <span class="identifier">ns</span>
|
||
<span class="identifier">QuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span><span class="identifier">_BigO</span> <span class="number">1.14</span> <span class="identifier">lgN</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">256</span> <span class="number">5.22</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">512</span> <span class="number">5.21</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">1024</span> <span class="number">5.21</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">2048</span> <span class="number">5.32</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">4096</span> <span class="number">5.33</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">8192</span> <span class="number">5.50</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">16384</span> <span class="number">5.74</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">32768</span> <span class="number">7.74</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">65536</span> <span class="number">10.6</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">131072</span> <span class="number">10.7</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">262144</span> <span class="number">10.6</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">524288</span> <span class="number">10.5</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">1048576</span> <span class="number">10.6</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermite</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span><span class="identifier">_BigO</span> <span class="number">7.57</span> <span class="special">(</span><span class="number">1</span><span class="special">)</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">256</span> <span class="number">5.27</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">512</span> <span class="number">5.26</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">1024</span> <span class="number">5.26</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">2048</span> <span class="number">5.28</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">4096</span> <span class="number">5.30</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">8192</span> <span class="number">5.41</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">16384</span> <span class="number">5.89</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">32768</span> <span class="number">5.97</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">65536</span> <span class="number">5.96</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">131072</span> <span class="number">5.92</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">262144</span> <span class="number">5.94</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">524288</span> <span class="number">5.96</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">>/</span><span class="number">1048576</span> <span class="number">5.93</span> <span class="identifier">ns</span>
|
||
<span class="identifier">CardinalQuinticHermiteAOS</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span><span class="identifier">_BigO</span> <span class="number">5.64</span> <span class="special">(</span><span class="number">1</span><span class="special">)</span>
|
||
</pre>
|
||
</div>
|
||
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
|
||
<td align="left"></td>
|
||
<td align="right"><div class="copyright-footer">Copyright © 2006-2021 Nikhar Agrawal, Anton Bikineev, Matthew Borland,
|
||
Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert Holin, Bruno
|
||
Lalande, John Maddock, Evan Miller, Jeremy Murphy, Matthew Pulver, Johan Råde,
|
||
Gautam Sewani, Benjamin Sobotta, Nicholas Thompson, Thijs van den Berg, Daryle
|
||
Walker and Xiaogang Zhang<p>
|
||
Distributed under the Boost Software License, Version 1.0. (See accompanying
|
||
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>)
|
||
</p>
|
||
</div></td>
|
||
</tr></table>
|
||
<hr>
|
||
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