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25 changes: 12 additions & 13 deletions classSplineBuilder-members.html
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<tr><td class="entry"><a class="el" href="classSplineBuilder.html#a60ece27168e990dd396dd059ce238267">operator()</a>(ddc::ChunkSpan&lt; double, ddc::DiscreteDomain&lt; bsplines_type &gt;&gt; spline, ddc::ChunkSpan&lt; double const, interpolation_domain_type &gt; vals, std::optional&lt; CDSpan1D &gt; const derivs_xmin=std::nullopt, std::optional&lt; CDSpan1D &gt; const derivs_xmax=std::nullopt) const</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>operator=</b>(SplineBuilder const &amp;x)=delete (defined in <a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a>)</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"></td></tr>
<tr><td class="entry"><a class="el" href="classSplineBuilder.html#a2763318a2269b27a7a051200bbc5b659">operator=</a>(SplineBuilder &amp;&amp;x)=default</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"></td></tr>
<tr class="even"><td class="entry"><a class="el" href="classSplineBuilder.html#adce1a4d93d232bc29f6c8482d7ecdd06">quadrature_coefficients</a>(ddc::DiscreteDomain&lt; IDim &gt; const &amp;domain) const noexcept</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
<tr><td class="entry"><a class="el" href="classSplineBuilder.html#aecdea9406e7d85496bf6ed4c479d064d">s_bc_xmax</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr class="even"><td class="entry"><a class="el" href="classSplineBuilder.html#a4d5e60f3a4050a4a54415835b65d03c8">s_bc_xmin</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr><td class="entry"><a class="el" href="classSplineBuilder.html#a750e366c0f6cff13ee6b09e84fbd7f39">s_nbc_xmax</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr class="even"><td class="entry"><a class="el" href="classSplineBuilder.html#ad95603fd1144bd421f0ab85c8e8985a8">s_nbc_xmin</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr><td class="entry"><a class="el" href="classSplineBuilder.html#ac37e871f135ba9da956d8faacff00032">s_nbe_xmax</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr class="even"><td class="entry"><a class="el" href="classSplineBuilder.html#a6e27acbbf2fc5f1400ce4a08c810d52e">s_nbe_xmin</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr><td class="entry"><a class="el" href="classSplineBuilder.html#a8c55b038757bcdf9ad2572897f4f836b">s_odd</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr class="even"><td class="entry"><a class="el" href="classSplineBuilder.html#a2d211caa5dd227dd6d05947484d1b6e9">spline_domain</a>() const noexcept</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
<tr><td class="entry"><a class="el" href="classSplineBuilder.html#aa1c79d6ada6f3253febfc994b9a2d55e">SplineBuilder</a>(interpolation_domain_type const &amp;interpolation_domain)</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"></td></tr>
<tr class="even"><td class="entry"><a class="el" href="classSplineBuilder.html#aff30d3c9ee7e83246b37719a0866874c">SplineBuilder</a>(SplineBuilder const &amp;x)=delete</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"></td></tr>
<tr><td class="entry"><a class="el" href="classSplineBuilder.html#ad62a92276f053ebdfcc38f1ede5b7198">SplineBuilder</a>(SplineBuilder &amp;&amp;x)=default</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0" class="even"><td class="entry"><b>~SplineBuilder</b>()=default (defined in <a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a>)</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"></td></tr>
<tr class="even"><td class="entry"><a class="el" href="classSplineBuilder.html#aecdea9406e7d85496bf6ed4c479d064d">s_bc_xmax</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr><td class="entry"><a class="el" href="classSplineBuilder.html#a4d5e60f3a4050a4a54415835b65d03c8">s_bc_xmin</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr class="even"><td class="entry"><a class="el" href="classSplineBuilder.html#a750e366c0f6cff13ee6b09e84fbd7f39">s_nbc_xmax</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr><td class="entry"><a class="el" href="classSplineBuilder.html#ad95603fd1144bd421f0ab85c8e8985a8">s_nbc_xmin</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr class="even"><td class="entry"><a class="el" href="classSplineBuilder.html#ac37e871f135ba9da956d8faacff00032">s_nbe_xmax</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr><td class="entry"><a class="el" href="classSplineBuilder.html#a6e27acbbf2fc5f1400ce4a08c810d52e">s_nbe_xmin</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr class="even"><td class="entry"><a class="el" href="classSplineBuilder.html#a8c55b038757bcdf9ad2572897f4f836b">s_odd</a></td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">static</span></td></tr>
<tr><td class="entry"><a class="el" href="classSplineBuilder.html#a2d211caa5dd227dd6d05947484d1b6e9">spline_domain</a>() const noexcept</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"><span class="mlabel">inline</span></td></tr>
<tr class="even"><td class="entry"><a class="el" href="classSplineBuilder.html#aa1c79d6ada6f3253febfc994b9a2d55e">SplineBuilder</a>(interpolation_domain_type const &amp;interpolation_domain)</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"></td></tr>
<tr><td class="entry"><a class="el" href="classSplineBuilder.html#aff30d3c9ee7e83246b37719a0866874c">SplineBuilder</a>(SplineBuilder const &amp;x)=delete</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"></td></tr>
<tr class="even"><td class="entry"><a class="el" href="classSplineBuilder.html#ad62a92276f053ebdfcc38f1ede5b7198">SplineBuilder</a>(SplineBuilder &amp;&amp;x)=default</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"></td></tr>
<tr bgcolor="#f0f0f0"><td class="entry"><b>~SplineBuilder</b>()=default (defined in <a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a>)</td><td class="entry"><a class="el" href="classSplineBuilder.html">SplineBuilder&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;</a></td><td class="entry"></td></tr>
</table></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
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<tr class="memitem:ab66639ab2f9529f4430ce60320eb9e17"><td class="memItemLeft" align="right" valign="top">const <a class="el" href="classMatrix.html">Matrix</a> &amp;&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classSplineBuilder.html#ab66639ab2f9529f4430ce60320eb9e17">get_interpolation_matrix</a> () const noexcept</td></tr>
<tr class="memdesc:ab66639ab2f9529f4430ce60320eb9e17"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the interpolation matrix. <a href="classSplineBuilder.html#ab66639ab2f9529f4430ce60320eb9e17">More...</a><br /></td></tr>
<tr class="separator:ab66639ab2f9529f4430ce60320eb9e17"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:adce1a4d93d232bc29f6c8482d7ecdd06"><td class="memTemplParams" colspan="2">template&lt;class IDim &gt; </td></tr>
<tr class="memitem:adce1a4d93d232bc29f6c8482d7ecdd06"><td class="memTemplItemLeft" align="right" valign="top">ddc::Chunk&lt; double, ddc::DiscreteDomain&lt; IDim &gt; &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="classSplineBuilder.html#adce1a4d93d232bc29f6c8482d7ecdd06">quadrature_coefficients</a> (ddc::DiscreteDomain&lt; IDim &gt; const &amp;domain) const noexcept</td></tr>
<tr class="memdesc:adce1a4d93d232bc29f6c8482d7ecdd06"><td class="mdescLeft">&#160;</td><td class="mdescRight">Get the spline quadrature coefficients. <a href="classSplineBuilder.html#adce1a4d93d232bc29f6c8482d7ecdd06">More...</a><br /></td></tr>
<tr class="separator:adce1a4d93d232bc29f6c8482d7ecdd06"><td class="memSeparator" colspan="2">&#160;</td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="pub-static-attribs"></a>
Static Public Attributes</h2></td></tr>
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<p>Get the interpolation matrix. This can be useful for debugging (as it allows one to print the matrix) or for more complex quadrature schemes.</p>
<dl class="section return"><dt>Returns</dt><dd>A reference to the interpolation matrix. </dd></dl>

</div>
</div>
<a id="adce1a4d93d232bc29f6c8482d7ecdd06"></a>
<h2 class="memtitle"><span class="permalink"><a href="#adce1a4d93d232bc29f6c8482d7ecdd06">&#9670;&nbsp;</a></span>quadrature_coefficients()</h2>

<div class="memitem">
<div class="memproto">
<div class="memtemplate">
template&lt;class BSplines , class interpolation_mesh_type , BoundCond BcXmin, BoundCond BcXmax&gt; </div>
<div class="memtemplate">
template&lt;class IDim &gt; </div>
<table class="mlabels">
<tr>
<td class="mlabels-left">
<table class="memname">
<tr>
<td class="memname">ddc::Chunk&lt;double, ddc::DiscreteDomain&lt;IDim&gt; &gt; <a class="el" href="classSplineBuilder.html">SplineBuilder</a>&lt; BSplines, interpolation_mesh_type, BcXmin, BcXmax &gt;::quadrature_coefficients </td>
<td>(</td>
<td class="paramtype">ddc::DiscreteDomain&lt; IDim &gt; const &amp;&#160;</td>
<td class="paramname"><em>domain</em></td><td>)</td>
<td> const</td>
</tr>
</table>
</td>
<td class="mlabels-right">
<span class="mlabels"><span class="mlabel">inline</span><span class="mlabel">noexcept</span></span> </td>
</tr>
</table>
</div><div class="memdoc">

<p>Get the spline quadrature coefficients. </p>
<p>To integrate a function with a spline quadrature, we use:</p>
<p>\( \int_a^b f(x)dx \simeq \sum_{i = 0}^{N_{\text{basis}} -1 } c_i \int_a^b b_{i,d}()x dx \),</p>
<p>which rewritten gives</p>
<p>\( \int_a^b f(x)dx \simeq \sum_{i = 0}^{N_{\text{basis}} - 1} q_i f_i \),</p>
<p>with</p><ul>
<li>\(\{ f_i\}_i \) the values of the function at the interpolation points;</li>
<li>\( q = \{ q_i\}_i \) the quadrature coefficients we compute thanks to \( q B^T = I_b \),<ul>
<li>with \( B \) the matrix of B-splines \( B_{ij} = b_{j,d}(x_i)\),</li>
<li>and \( I_b = \int_a^b b_{i,d}(x)dx \) the integrated B-splines.</li>
</ul>
</li>
</ul>
<p>More details are given in Emily Bourne's thesis "Non-Uniform Numerical Schemes for the Modelling of Turbulence
in the 5D GYSELA Code". December 2022.</p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramdir">[in]</td><td class="paramname">domain</td><td>The domain where the functions we want to integrate are defined.</td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>A chunk with the quadrature coefficients \( q \). </dd></dl>

</div>
</div>
<h2 class="groupheader">Member Data Documentation</h2>
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3 changes: 1 addition & 2 deletions classSplineBuilder.js
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