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Buggy, must check why interpolator assignment destroys precomputed data.
author Jordi Guitérrez Hermoso <jordigh@gmail.com>
date Sun, 29 Jun 2008 04:06:48 -0500
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<h1>rbf::radial_basis_function Class Reference</h1><!-- doxytag: class="rbf::radial_basis_function" --><!-- doxytag: inherits="bvp::realfunc" -->Base abstract class.  
<a href="#_details">More...</a>
<p>
<code>#include &lt;<a class="el" href="rbf_8hpp-source.html">rbf.hpp</a>&gt;</code>
<p>
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Inheritance diagram for rbf::radial_basis_function:</div>
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Collaboration diagram for rbf::radial_basis_function:</div>
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<p>
<a href="classrbf_1_1radial__basis__function-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
<tr><td></td></tr>
<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#7265d98eded627fe04c765bfce215d25">radial_basis_function</a> ()</td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default constructor, centred at zero by default.  <a href="#7265d98eded627fe04c765bfce215d25"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#4b7edf55b630a5ada859c5184d133b11">~radial_basis_function</a> ()</td></tr>

<tr><td class="memItemLeft" nowrap align="right" valign="top">&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#8b3b14a3218fb2c8f8cc684f65b4e330">radial_basis_function</a> (const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;c)</td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Specify the point where this <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> is centred.  <a href="#8b3b14a3218fb2c8f8cc684f65b4e330"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#ae1eb324111681a206e7d1c082d29375">set_centre</a> (const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;c)</td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Specify the point where this <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> is centred.  <a href="#ae1eb324111681a206e7d1c082d29375"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#7e15c696294ee0971996a69e81ad47f5">at</a> (const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;x) const </td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Evaluate <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> at x.  <a href="#7e15c696294ee0971996a69e81ad47f5"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#f84cf36f465a2b3aca612c7f9aff4a4d">operator()</a> (const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;x) const </td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Evaluate <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> at x.  <a href="#f84cf36f465a2b3aca612c7f9aff4a4d"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#e0636c1b889e738eaebee62a4bfb3089">d</a> (const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;x, size_t k) const </td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">First partial derivative at x in direction k;.  <a href="#e0636c1b889e738eaebee62a4bfb3089"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#dc48320c73294ab16da27e7449e9fae1">d2</a> (const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;x, size_t k1, size_t k2) const </td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Second derivative at x in directions k1 and k2.  <a href="#dc48320c73294ab16da27e7449e9fae1"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#00bdf1d0544fe1a304ed69ecbb1abec8">operator&lt;</a> (const <a class="el" href="classrbf_1_1radial__basis__function.html">radial_basis_function</a> &amp;phi) const </td></tr>

<tr><td colspan="2"><br><h2>Static Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">static void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#c375947330d9708fa249c846264a0b7d">set_dimension</a> (size_t dim)</td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Specify the dimension of all rbf's.  <a href="#c375947330d9708fa249c846264a0b7d"></a><br></td></tr>
<tr><td colspan="2"><br><h2>Protected Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#ca1d152380fa43082c710a07f28080be">operator()</a> (double r) const =0</td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">The scalar functions defining each RBF.  <a href="#ca1d152380fa43082c710a07f28080be"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#0aa55b82614330604e8ea63b8aef419a">d</a> (double r) const =0</td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">The scalar first derivative defining each RBF.  <a href="#0aa55b82614330604e8ea63b8aef419a"></a><br></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#97c9b2a2a93d7133d57cbecf7c3996ac">d2</a> (double r) const =0</td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">The scalar second derivative defining each RBF.  <a href="#97c9b2a2a93d7133d57cbecf7c3996ac"></a><br></td></tr>
<tr><td colspan="2"><br><h2>Private Member Functions</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#61987d4f7f2ccca9cea3d26416ff089a">bad_dimension</a> (string file, int line, size_t dim) const </td></tr>

<tr><td colspan="2"><br><h2>Private Attributes</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classlinalg_1_1vector.html">point</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8">centre</a></td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Point on which this <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> is centred.  <a href="#5f8d4f932217b0941a14597dc829c6a8"></a><br></td></tr>
<tr><td colspan="2"><br><h2>Static Private Attributes</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">static size_t&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8">dimension</a> = 0</td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Dimensionality of all rbfs.  <a href="#feaea7326abce992e883fad2469731e8"></a><br></td></tr>
<tr><td colspan="2"><br><h2>Friends</h2></td></tr>
<tr><td class="memItemLeft" nowrap align="right" valign="top">size_t&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classrbf_1_1radial__basis__function.html#52f84ac14341083846f4a18e017ced95">hash_value</a> (const <a class="el" href="classrbf_1_1radial__basis__function.html">radial_basis_function</a> &amp;)</td></tr>

<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">An <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> hash function.  <a href="#52f84ac14341083846f4a18e017ced95"></a><br></td></tr>
</table>
<hr><a name="_details"></a><h2>Detailed Description</h2>
Base abstract class. <hr><h2>Constructor &amp; Destructor Documentation</h2>
<a class="anchor" name="7265d98eded627fe04c765bfce215d25"></a><!-- doxytag: member="rbf::radial_basis_function::radial_basis_function" ref="7265d98eded627fe04c765bfce215d25" args="()" -->
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          <td class="memname">rbf::radial_basis_function::radial_basis_function           </td>
          <td>(</td>
          <td class="paramname">          </td>
          <td>&nbsp;)&nbsp;</td>
          <td></td>
        </tr>
      </table>
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<div class="memdoc">

<p>
Default constructor, centred at zero by default. 
<p>
<div class="fragment"><pre class="fragment"><a name="l00022"></a>00022                                               {
<a name="l00023"></a>00023     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a> != 0){
<a name="l00024"></a>00024       <a class="code" href="namespacelinalg.html#93d09321b3ca781d34e48a484ac7da60" title="Useful alias, vectors are also points in space.">point</a> zero(<a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a>); <span class="comment">//Centred by default at the origin.</span>
<a name="l00025"></a>00025       <a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a> = zero;
<a name="l00026"></a>00026     }
<a name="l00027"></a>00027   }
</pre></div>
<p>

</div>
</div><p>
<a class="anchor" name="4b7edf55b630a5ada859c5184d133b11"></a><!-- doxytag: member="rbf::radial_basis_function::~radial_basis_function" ref="4b7edf55b630a5ada859c5184d133b11" args="()" -->
<div class="memitem">
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        <tr>
          <td class="memname">rbf::radial_basis_function::~radial_basis_function           </td>
          <td>(</td>
          <td class="paramname">          </td>
          <td>&nbsp;)&nbsp;</td>
          <td><code> [virtual]</code></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>
<div class="fragment"><pre class="fragment"><a name="l00036"></a>00036                                                {
<a name="l00037"></a>00037     <span class="comment">//Nothing to destroy!</span>
<a name="l00038"></a>00038   }
</pre></div>
<p>

</div>
</div><p>
<a class="anchor" name="8b3b14a3218fb2c8f8cc684f65b4e330"></a><!-- doxytag: member="rbf::radial_basis_function::radial_basis_function" ref="8b3b14a3218fb2c8f8cc684f65b4e330" args="(const point &amp;c)" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
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          <td class="memname">rbf::radial_basis_function::radial_basis_function           </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;&nbsp;</td>
          <td class="paramname"> <em>c</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>
Specify the point where this <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> is centred. 
<p>
<div class="fragment"><pre class="fragment"><a name="l00029"></a>00029                                                             {
<a name="l00030"></a>00030     <span class="keywordflow">if</span>(c.size() != <a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a>)
<a name="l00031"></a>00031       <a class="code" href="classrbf_1_1radial__basis__function.html#61987d4f7f2ccca9cea3d26416ff089a">bad_dimension</a>(__FILE__, __LINE__, c.size());
<a name="l00032"></a>00032     <span class="keywordflow">else</span>
<a name="l00033"></a>00033       <a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a> = c;
<a name="l00034"></a>00034   }
</pre></div>
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<p>
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</div>
</div><p>
<hr><h2>Member Function Documentation</h2>
<a class="anchor" name="c375947330d9708fa249c846264a0b7d"></a><!-- doxytag: member="rbf::radial_basis_function::set_dimension" ref="c375947330d9708fa249c846264a0b7d" args="(size_t dim)" -->
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          <td class="memname">void rbf::radial_basis_function::set_dimension           </td>
          <td>(</td>
          <td class="paramtype">size_t&nbsp;</td>
          <td class="paramname"> <em>dim</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td><code> [static]</code></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>
Specify the dimension of all rbf's. 
<p>
<div class="fragment"><pre class="fragment"><a name="l00047"></a>00047                                                      {
<a name="l00048"></a>00048     <a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a> = dim;
<a name="l00049"></a>00049   }
</pre></div>
<p>

</div>
</div><p>
<a class="anchor" name="ae1eb324111681a206e7d1c082d29375"></a><!-- doxytag: member="rbf::radial_basis_function::set_centre" ref="ae1eb324111681a206e7d1c082d29375" args="(const point &amp;c)" -->
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          <td class="memname">void rbf::radial_basis_function::set_centre           </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;&nbsp;</td>
          <td class="paramname"> <em>c</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td></td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>
Specify the point where this <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> is centred. 
<p>
<div class="fragment"><pre class="fragment"><a name="l00040"></a>00040                                                       {
<a name="l00041"></a>00041     <span class="keywordflow">if</span>(c.size () != <a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a>)
<a name="l00042"></a>00042       <a class="code" href="classrbf_1_1radial__basis__function.html#61987d4f7f2ccca9cea3d26416ff089a">bad_dimension</a>(__FILE__, __LINE__, c.size());
<a name="l00043"></a>00043     <span class="keywordflow">else</span>
<a name="l00044"></a>00044       <a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a> = c;
<a name="l00045"></a>00045   }
</pre></div>
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<a class="anchor" name="7e15c696294ee0971996a69e81ad47f5"></a><!-- doxytag: member="rbf::radial_basis_function::at" ref="7e15c696294ee0971996a69e81ad47f5" args="(const point &amp;x) const " -->
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          <td class="memname">double rbf::radial_basis_function::at           </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;&nbsp;</td>
          <td class="paramname"> <em>x</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td> const</td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>
Evaluate <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> at x. 
<p>
<div class="fragment"><pre class="fragment"><a name="l00071"></a>00071                                                       {
<a name="l00072"></a>00072     <span class="keywordflow">return</span> <a class="code" href="classrbf_1_1radial__basis__function.html#f84cf36f465a2b3aca612c7f9aff4a4d" title="Evaluate rbf at x.">operator()</a>(x);
<a name="l00073"></a>00073   }
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<a class="anchor" name="f84cf36f465a2b3aca612c7f9aff4a4d"></a><!-- doxytag: member="rbf::radial_basis_function::operator()" ref="f84cf36f465a2b3aca612c7f9aff4a4d" args="(const point &amp;x) const " -->
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          <td class="memname">double rbf::radial_basis_function::operator()           </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;&nbsp;</td>
          <td class="paramname"> <em>x</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td> const</td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>
Evaluate <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> at x. 
<p>
<div class="fragment"><pre class="fragment"><a name="l00075"></a>00075                                                               {
<a name="l00076"></a>00076     <span class="keywordflow">if</span>(x.size() != <a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a>)
<a name="l00077"></a>00077       <a class="code" href="classrbf_1_1radial__basis__function.html#61987d4f7f2ccca9cea3d26416ff089a">bad_dimension</a>(__FILE__, __LINE__, x.size());
<a name="l00078"></a>00078     <span class="keywordflow">return</span> <a class="code" href="classrbf_1_1radial__basis__function.html#f84cf36f465a2b3aca612c7f9aff4a4d" title="Evaluate rbf at x.">operator()</a>( <a class="code" href="namespacelinalg.html#47d0ccf60c6c93a9dda16d9e9a0ef965" title="Euclidean norm of a vector.">norm</a>(x - <a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a>) );
<a name="l00079"></a>00079   }
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<a class="anchor" name="e0636c1b889e738eaebee62a4bfb3089"></a><!-- doxytag: member="rbf::radial_basis_function::d" ref="e0636c1b889e738eaebee62a4bfb3089" args="(const point &amp;x, size_t k) const " -->
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          <td class="memname">double rbf::radial_basis_function::d           </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;&nbsp;</td>
          <td class="paramname"> <em>x</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">size_t&nbsp;</td>
          <td class="paramname"> <em>k</em></td><td>&nbsp;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td><td> const</td>
        </tr>
      </table>
</div>
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<p>
First partial derivative at x in direction k;. 
<p>
<div class="fragment"><pre class="fragment"><a name="l00081"></a>00081                                                                {
<a name="l00082"></a>00082     <span class="keywordflow">if</span>(x.size() != <a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a>)
<a name="l00083"></a>00083       <a class="code" href="classrbf_1_1radial__basis__function.html#61987d4f7f2ccca9cea3d26416ff089a">bad_dimension</a>(__FILE__, __LINE__, x.size());
<a name="l00084"></a>00084     <span class="keywordflow">else</span> <span class="keywordflow">if</span>(k &lt; 1 or k &gt; <a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a>){
<a name="l00085"></a>00085       <a class="code" href="structerror__handling_1_1badArgument.html" title="GSL_EINVAL = 4, /* invalid argument supplied by user */.">error_handling::badArgument</a> exc;
<a name="l00086"></a>00086       exc.<a class="code" href="classerror__handling_1_1error.html#717c6a821a336de7a830ab10afee7e73">reason</a> = <span class="stringliteral">"Cannot differentiate wrt given index: out of bounds."</span>;
<a name="l00087"></a>00087       exc.<a class="code" href="classerror__handling_1_1error.html#529da3a7e791062f68abe0877b741acd">line</a> = __LINE__;
<a name="l00088"></a>00088       exc.<a class="code" href="classerror__handling_1_1error.html#c1f9d103deb788c469e47f6066d4927f">file</a> = __FILE__;
<a name="l00089"></a>00089        <span class="keywordflow">throw</span> exc;
<a name="l00090"></a>00090     }
<a name="l00091"></a>00091     <span class="keywordflow">else</span> <span class="keywordflow">if</span>(x == <a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a>)
<a name="l00092"></a>00092       <span class="keywordflow">return</span> <a class="code" href="classrbf_1_1radial__basis__function.html#e0636c1b889e738eaebee62a4bfb3089" title="First partial derivative at x in direction k;.">d</a>(0);
<a name="l00093"></a>00093 
<a name="l00094"></a>00094     <span class="keywordtype">double</span> r = <a class="code" href="namespacelinalg.html#47d0ccf60c6c93a9dda16d9e9a0ef965" title="Euclidean norm of a vector.">norm</a>(x - <a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a>);
<a name="l00095"></a>00095     <span class="comment">//Call virtualised derived class function.</span>
<a name="l00096"></a>00096     <span class="keywordtype">double</span> result = <a class="code" href="classrbf_1_1radial__basis__function.html#e0636c1b889e738eaebee62a4bfb3089" title="First partial derivative at x in direction k;.">d</a>(r)*(x(k) - <a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a>(k))/r; 
<a name="l00097"></a>00097     <span class="keywordflow">return</span> result;
<a name="l00098"></a>00098   }
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<a class="anchor" name="dc48320c73294ab16da27e7449e9fae1"></a><!-- doxytag: member="rbf::radial_basis_function::d2" ref="dc48320c73294ab16da27e7449e9fae1" args="(const point &amp;x, size_t k1, size_t k2) const " -->
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          <td class="memname">double rbf::radial_basis_function::d2           </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classlinalg_1_1vector.html">point</a> &amp;&nbsp;</td>
          <td class="paramname"> <em>x</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">size_t&nbsp;</td>
          <td class="paramname"> <em>k1</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">size_t&nbsp;</td>
          <td class="paramname"> <em>k2</em></td><td>&nbsp;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td><td> const</td>
        </tr>
      </table>
</div>
<div class="memdoc">

<p>
Second derivative at x in directions k1 and k2. 
<p>
<div class="fragment"><pre class="fragment"><a name="l00101"></a>00101                                                               {
<a name="l00102"></a>00102     <span class="keywordflow">if</span>(x.size() != <a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a>)
<a name="l00103"></a>00103       <a class="code" href="classrbf_1_1radial__basis__function.html#61987d4f7f2ccca9cea3d26416ff089a">bad_dimension</a>(__FILE__, __LINE__, x.size());
<a name="l00104"></a>00104     <span class="keywordflow">else</span> <span class="keywordflow">if</span>(k1 &lt; 1 or k1 &gt; <a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a> or k2 &lt; 1 or k2 &gt; <a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a>){
<a name="l00105"></a>00105       <a class="code" href="structerror__handling_1_1badArgument.html" title="GSL_EINVAL = 4, /* invalid argument supplied by user */.">error_handling::badArgument</a> exc;
<a name="l00106"></a>00106       exc.<a class="code" href="classerror__handling_1_1error.html#717c6a821a336de7a830ab10afee7e73">reason</a> = <span class="stringliteral">"Cannot differentiate wrt given indices: out of bounds."</span>;
<a name="l00107"></a>00107       exc.<a class="code" href="classerror__handling_1_1error.html#529da3a7e791062f68abe0877b741acd">line</a> = __LINE__;
<a name="l00108"></a>00108       exc.<a class="code" href="classerror__handling_1_1error.html#c1f9d103deb788c469e47f6066d4927f">file</a> = __FILE__;
<a name="l00109"></a>00109       <span class="keywordflow">throw</span> exc;
<a name="l00110"></a>00110     }
<a name="l00111"></a>00111     <span class="keywordflow">else</span> <span class="keywordflow">if</span>(x == <a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a> and k1 == k2)
<a name="l00112"></a>00112       <span class="keywordflow">return</span> <a class="code" href="classrbf_1_1radial__basis__function.html#dc48320c73294ab16da27e7449e9fae1" title="Second derivative at x in directions k1 and k2.">d2</a>(0);
<a name="l00113"></a>00113     <span class="keywordflow">else</span> <span class="keywordflow">if</span>(x == <a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a> and k1 != k2)
<a name="l00114"></a>00114       <span class="keywordflow">return</span> 0;
<a name="l00115"></a>00115     <span class="keywordflow">else</span> <span class="keywordflow">if</span>(k1 != k2){
<a name="l00116"></a>00116       <span class="keywordtype">double</span> r = <a class="code" href="namespacelinalg.html#47d0ccf60c6c93a9dda16d9e9a0ef965" title="Euclidean norm of a vector.">norm</a>(x-<a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a>);
<a name="l00117"></a>00117       <span class="keywordtype">double</span> r2 = r*r;
<a name="l00118"></a>00118       <span class="keywordtype">double</span> top = (x(k1) - <a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a>(k1)) * (x(k2)-<a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a>(k2));
<a name="l00119"></a>00119       <span class="keywordflow">return</span>   
<a name="l00120"></a>00120         top * <a class="code" href="classrbf_1_1radial__basis__function.html#dc48320c73294ab16da27e7449e9fae1" title="Second derivative at x in directions k1 and k2.">d2</a>(r) / r2 -
<a name="l00121"></a>00121         top * <a class="code" href="classrbf_1_1radial__basis__function.html#e0636c1b889e738eaebee62a4bfb3089" title="First partial derivative at x in direction k;.">d</a>(r) / (r2*r);
<a name="l00122"></a>00122     }
<a name="l00123"></a>00123     <span class="keywordtype">double</span> r = <a class="code" href="namespacelinalg.html#47d0ccf60c6c93a9dda16d9e9a0ef965" title="Euclidean norm of a vector.">norm</a>(x-<a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a>);
<a name="l00124"></a>00124     <span class="keywordtype">double</span> r2 = r*r;
<a name="l00125"></a>00125     <span class="keywordtype">double</span> top = x(k1) - <a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a>(k1); top = top*top;
<a name="l00126"></a>00126     <span class="keywordtype">double</span> result =  top*<a class="code" href="classrbf_1_1radial__basis__function.html#dc48320c73294ab16da27e7449e9fae1" title="Second derivative at x in directions k1 and k2.">d2</a>(r)/r2  +  <a class="code" href="classrbf_1_1radial__basis__function.html#e0636c1b889e738eaebee62a4bfb3089" title="First partial derivative at x in direction k;.">d</a>(r)/r  -  top*<a class="code" href="classrbf_1_1radial__basis__function.html#e0636c1b889e738eaebee62a4bfb3089" title="First partial derivative at x in direction k;.">d</a>(r)/(r2*r);
<a name="l00127"></a>00127     <span class="keywordflow">return</span> result;
<a name="l00128"></a>00128     
<a name="l00129"></a>00129   }
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<a class="anchor" name="00bdf1d0544fe1a304ed69ecbb1abec8"></a><!-- doxytag: member="rbf::radial_basis_function::operator&lt;" ref="00bdf1d0544fe1a304ed69ecbb1abec8" args="(const radial_basis_function &amp;phi) const " -->
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          <td class="memname">bool rbf::radial_basis_function::operator&lt;           </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classrbf_1_1radial__basis__function.html">radial_basis_function</a> &amp;&nbsp;</td>
          <td class="paramname"> <em>phi</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td> const</td>
        </tr>
      </table>
</div>
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<p>
<div class="fragment"><pre class="fragment"><a name="l00142"></a>00142   {
<a name="l00143"></a>00143     <span class="keywordflow">return</span> (this-&gt;<a class="code" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8" title="Point on which this rbf is centred.">centre</a>) &lt; phi.centre;
<a name="l00144"></a>00144   }
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<a class="anchor" name="ca1d152380fa43082c710a07f28080be"></a><!-- doxytag: member="rbf::radial_basis_function::operator()" ref="ca1d152380fa43082c710a07f28080be" args="(double r) const =0" -->
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          <td class="memname">virtual double rbf::radial_basis_function::operator()           </td>
          <td>(</td>
          <td class="paramtype">double&nbsp;</td>
          <td class="paramname"> <em>r</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td> const<code> [protected, pure virtual]</code></td>
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<p>
The scalar functions defining each RBF. 
<p>

<p>Implemented in <a class="el" href="classrbf_1_1piecewise__polynomial.html#3f27fcfdc6d1eae838f1d713658bf3fe">rbf::piecewise_polynomial</a>, <a class="el" href="classrbf_1_1thin__plate__spline.html#bbdcc07f10356ae80eca1f2f789ef8cc">rbf::thin_plate_spline</a>, <a class="el" href="classrbf_1_1multiquadric.html#7c59d0aac328123b4d10c13d2d7b9c52">rbf::multiquadric</a>, <a class="el" href="classrbf_1_1inverse__multiquadric.html#48dd507964583baf313c14c46dd43938">rbf::inverse_multiquadric</a>, <a class="el" href="classrbf_1_1inverse__quadratic.html#2b9ddfbe44607a39d1530c830fd3c88f">rbf::inverse_quadratic</a>, and <a class="el" href="classrbf_1_1gaussian.html#ebecc13ca122f36fd95d7f9bc347a91e">rbf::gaussian</a>.</p>

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<a class="anchor" name="0aa55b82614330604e8ea63b8aef419a"></a><!-- doxytag: member="rbf::radial_basis_function::d" ref="0aa55b82614330604e8ea63b8aef419a" args="(double r) const =0" -->
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          <td class="memname">virtual double rbf::radial_basis_function::d           </td>
          <td>(</td>
          <td class="paramtype">double&nbsp;</td>
          <td class="paramname"> <em>r</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td> const<code> [protected, pure virtual]</code></td>
        </tr>
      </table>
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<div class="memdoc">

<p>
The scalar first derivative defining each RBF. 
<p>

<p>Implemented in <a class="el" href="classrbf_1_1piecewise__polynomial.html#f362c5d7e96e2d9c1dfabe3e2c65498f">rbf::piecewise_polynomial</a>, <a class="el" href="classrbf_1_1thin__plate__spline.html#9033e98e17d9689d5815228089b7895c">rbf::thin_plate_spline</a>, <a class="el" href="classrbf_1_1multiquadric.html#dbd3d5ff4ad64d8ee006641216d93e62">rbf::multiquadric</a>, <a class="el" href="classrbf_1_1inverse__multiquadric.html#3550ec37ec63f6ab020ec6508270b4c2">rbf::inverse_multiquadric</a>, <a class="el" href="classrbf_1_1inverse__quadratic.html#adc471cc4f1388a43e1574f78cad224f">rbf::inverse_quadratic</a>, and <a class="el" href="classrbf_1_1gaussian.html#af74dfa24625e952f3ed28b50cb5168d">rbf::gaussian</a>.</p>

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<a class="anchor" name="97c9b2a2a93d7133d57cbecf7c3996ac"></a><!-- doxytag: member="rbf::radial_basis_function::d2" ref="97c9b2a2a93d7133d57cbecf7c3996ac" args="(double r) const =0" -->
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          <td class="memname">virtual double rbf::radial_basis_function::d2           </td>
          <td>(</td>
          <td class="paramtype">double&nbsp;</td>
          <td class="paramname"> <em>r</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td> const<code> [protected, pure virtual]</code></td>
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      </table>
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<p>
The scalar second derivative defining each RBF. 
<p>

<p>Implemented in <a class="el" href="classrbf_1_1piecewise__polynomial.html#3732b85454de689672b2a130260755de">rbf::piecewise_polynomial</a>, <a class="el" href="classrbf_1_1thin__plate__spline.html#e58fdc6d240f0146ef418507af2bc29d">rbf::thin_plate_spline</a>, <a class="el" href="classrbf_1_1multiquadric.html#06ad074df875614c2c38f040607811a0">rbf::multiquadric</a>, <a class="el" href="classrbf_1_1inverse__multiquadric.html#32381ac78a5100e910deceb972f34eb0">rbf::inverse_multiquadric</a>, <a class="el" href="classrbf_1_1inverse__quadratic.html#fcfd3505bfd384a1519e8fa50b4ebe9f">rbf::inverse_quadratic</a>, and <a class="el" href="classrbf_1_1gaussian.html#991123e6a209bf7308904fb390d55938">rbf::gaussian</a>.</p>

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<a class="anchor" name="61987d4f7f2ccca9cea3d26416ff089a"></a><!-- doxytag: member="rbf::radial_basis_function::bad_dimension" ref="61987d4f7f2ccca9cea3d26416ff089a" args="(string file, int line, size_t dim) const " -->
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          <td class="memname">void rbf::radial_basis_function::bad_dimension           </td>
          <td>(</td>
          <td class="paramtype">string&nbsp;</td>
          <td class="paramname"> <em>file</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">int&nbsp;</td>
          <td class="paramname"> <em>line</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">size_t&nbsp;</td>
          <td class="paramname"> <em>dim</em></td><td>&nbsp;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td><td> const<code> [private]</code></td>
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<p>
In case we attempt to give this <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> an argument of the wrong dimension. <div class="fragment"><pre class="fragment"><a name="l00052"></a>00052                                                                        {
<a name="l00053"></a>00053     <a class="code" href="structerror__handling_1_1badDimension.html" title="An exception struct for RBFs when attempting to use the wrong dimension.">error_handling::badDimension</a> exc;
<a name="l00054"></a>00054     <span class="keywordflow">if</span>(<a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a> == 0)
<a name="l00055"></a>00055       exc.<a class="code" href="classerror__handling_1_1error.html#717c6a821a336de7a830ab10afee7e73">reason</a> = 
<a name="l00056"></a>00056         <span class="stringliteral">"Vector of wrong dimensionality passed to "</span>
<a name="l00057"></a>00057         <span class="stringliteral">"radial basis function. \n"</span> 
<a name="l00058"></a>00058         <span class="stringliteral">"(Did you forget to set the dimension?)"</span>;
<a name="l00059"></a>00059     <span class="keywordflow">else</span>
<a name="l00060"></a>00060       exc.<a class="code" href="classerror__handling_1_1error.html#717c6a821a336de7a830ab10afee7e73">reason</a> = 
<a name="l00061"></a>00061         <span class="stringliteral">"Vector of wrong dimensionality passed to "</span>
<a name="l00062"></a>00062         <span class="stringliteral">"radial basis function."</span>;      
<a name="l00063"></a>00063 
<a name="l00064"></a>00064     exc.<a class="code" href="classerror__handling_1_1error.html#529da3a7e791062f68abe0877b741acd">line</a> = line;
<a name="l00065"></a>00065     exc.<a class="code" href="classerror__handling_1_1error.html#c1f9d103deb788c469e47f6066d4927f">file</a> = file;
<a name="l00066"></a>00066     exc.<a class="code" href="structerror__handling_1_1badDimension.html#8a9b25ac3f6805e32a443f0863e5a2ca">given_dimension</a> = dim;
<a name="l00067"></a>00067     exc.<a class="code" href="structerror__handling_1_1badDimension.html#cd16cd048b8ba75fa68fbed34a9153b0">actual_dimension</a> = <a class="code" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8" title="Dimensionality of all rbfs.">dimension</a>;
<a name="l00068"></a>00068     <span class="keywordflow">throw</span> exc;
<a name="l00069"></a>00069   }
</pre></div>
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<hr><h2>Friends And Related Function Documentation</h2>
<a class="anchor" name="52f84ac14341083846f4a18e017ced95"></a><!-- doxytag: member="rbf::radial_basis_function::hash_value" ref="52f84ac14341083846f4a18e017ced95" args="(const radial_basis_function &amp;)" -->
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          <td class="memname">size_t hash_value           </td>
          <td>(</td>
          <td class="paramtype">const <a class="el" href="classrbf_1_1radial__basis__function.html">radial_basis_function</a> &amp;&nbsp;</td>
          <td class="paramname"> <em>phi</em>          </td>
          <td>&nbsp;)&nbsp;</td>
          <td><code> [friend]</code></td>
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An <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> hash function. 
<p>
<div class="fragment"><pre class="fragment"><a name="l00132"></a>00132   {
<a name="l00133"></a>00133     <span class="keywordtype">size_t</span> seed = 0;
<a name="l00134"></a>00134     <span class="keyword">using namespace </span>boost;
<a name="l00135"></a>00135     <span class="keywordflow">for</span>(<span class="keywordtype">size_t</span> i = 1; i &lt;= phi.centre.size(); i++)
<a name="l00136"></a>00136       hash_combine(seed,phi.centre(i));
<a name="l00137"></a>00137     hash_combine(seed,<span class="keyword">typeid</span>(phi).name());
<a name="l00138"></a>00138     <span class="keywordflow">return</span> seed;
<a name="l00139"></a>00139   }
</pre></div>
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<hr><h2>Member Data Documentation</h2>
<a class="anchor" name="5f8d4f932217b0941a14597dc829c6a8"></a><!-- doxytag: member="rbf::radial_basis_function::centre" ref="5f8d4f932217b0941a14597dc829c6a8" args="" -->
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          <td class="memname"><a class="el" href="classlinalg_1_1vector.html">point</a> <a class="el" href="classrbf_1_1radial__basis__function.html#5f8d4f932217b0941a14597dc829c6a8">rbf::radial_basis_function::centre</a><code> [private]</code>          </td>
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<p>
Point on which this <a class="el" href="namespacerbf.html" title="Radial basis function namespace.">rbf</a> is centred. 
<p>

</div>
</div><p>
<a class="anchor" name="feaea7326abce992e883fad2469731e8"></a><!-- doxytag: member="rbf::radial_basis_function::dimension" ref="feaea7326abce992e883fad2469731e8" args="" -->
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          <td class="memname">size_t <a class="el" href="classrbf_1_1radial__basis__function.html#feaea7326abce992e883fad2469731e8">rbf::radial_basis_function::dimension</a> = 0<code> [static, private]</code>          </td>
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<p>
Dimensionality of all rbfs. 
<p>

</div>
</div><p>
<hr>The documentation for this class was generated from the following files:<ul>
<li>include/<a class="el" href="rbf_8hpp-source.html">rbf.hpp</a><li><a class="el" href="rbf_8cpp.html">rbf.cpp</a></ul>
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