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<!DOCTYPE html>
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<title>dip::CovarianceMatrix class | DIPlib | a library for quantitative image analysis</title>
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<a href="https://diplib.org"><img src="DIPlib_logo.svg" alt="" />DIPlib</a><span class="m-breadcrumb">┃</span><a href="index.html" class="m-thin">a library for quantitative image analysis</a><span class="m-breadcrumb">┃</span><a href="https://github.com/DIPlib/diplib/releases/tag/3.5.2" class="m-thin">version 3.5.2</a> </span>
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<h1>
<div class="m-doc-include m-thin m-right-m m-text-right">
<a href="measurement.html" class="m-doc">Measurement</a> module<br/><span class="m-code m-thin">#include <a href="file--diplib--chain_code-h.html">"diplib/chain_code.h"</a></span> </div>
<span class="m-breadcrumb"><a href="dip.html">dip</a>::<wbr/></span>CovarianceMatrix <span class="m-thin">class</span> </h1>
<p>A 2D covariance matrix for computation with 2D vertices.</p>
<div class="m-block m-default">
<h3>Contents</h3>
<ul>
<li>
Reference
<ul>
<li><a href="#typeless-methods">Constructors, destructors, assignment and conversion operators</a></li>
<li><a href="#nested-classes">Classes</a></li>
<li><a href="#function-members">Functions</a></li>
<li><a href="#operator-members">Operators</a></li>
</ul>
</li>
</ul>
</div>
<p>The matrix is real, symmetric, positive semidefinite. See <a href="#dip-Polygon-CovarianceMatrix-VertexFloat-CL-C"><code>dip::Polygon::CovarianceMatrix</code></a>
for how to create a covariance matrix.</p>
<p>The elements stored are <code>xx</code>, <code>xy</code> and <code>yy</code>, with <code>xx</code> the top-left element, and <code>xy</code> both
the off-diagonal elements, which are equal by definition.</p>
<section id="typeless-methods">
<h2>Constructors, destructors, assignment and conversion operators</h2>
<dl class="m-doc">
<dt id="dip-CovarianceMatrix-CovarianceMatrix">
<span class="m-doc-wrap-bumper"><a href="#dip-CovarianceMatrix-CovarianceMatrix" class="m-doc-self">CovarianceMatrix</a>(</span><span class="m-doc-wrap">) <span class="m-label m-flat m-info">defaulted</span></span>
</dt>
<dd>Default-initialized covariance matrix is all zeros.</dd>
<dt id="dip-CovarianceMatrix-CovarianceMatrix-VertexFloat-">
<span class="m-doc-wrap-bumper"><a href="#dip-CovarianceMatrix-CovarianceMatrix-VertexFloat-" class="m-doc-self">CovarianceMatrix</a>(</span><span class="m-doc-wrap"><a href="dip-Vertex-T.html#dip-VertexFloat" class="m-doc">dip::VertexFloat</a> v) <span class="m-label m-flat m-info">explicit</span> </span>
</dt>
<dd>Construct a covariance matrix as the outer product of a vector and itself.</dd>
<dt id="dip-CovarianceMatrix-CovarianceMatrix-dfloat--dfloat--dfloat-">
<span class="m-doc-wrap-bumper"><a href="#dip-CovarianceMatrix-CovarianceMatrix-dfloat--dfloat--dfloat-" class="m-doc-self">CovarianceMatrix</a>(</span><span class="m-doc-wrap"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> xx,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> yy,
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> xy) <span class="m-label m-flat m-info">explicit</span> </span>
</dt>
<dd>Construct a covariance matrix with the three components.</dd>
</dl>
</section>
<section id="nested-classes">
<h2>Classes</h2>
<dl class="m-doc">
<dt>
struct <a href="dip-CovarianceMatrix-Eigenvalues.html" class="m-doc">Eigenvalues</a>
</dt>
<dd>Container for matrix eigenvalues.</dd>
<dt>
struct <a href="#dip-CovarianceMatrix-EllipseParameters" class="m-doc">EllipseParameters</a>
</dt>
<dd>Container for ellipse parameters. <a href="#dip-CovarianceMatrix-EllipseParameters">more...</a></dd>
</dl>
</section>
<section id="function-members">
<h2>Functions</h2>
<dl class="m-doc">
<dt id="dip-CovarianceMatrix-xx-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-CovarianceMatrix-xx-C" class="m-doc-self">xx</a>(</span><span class="m-doc-wrap">) const -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a></span>
</dt>
<dd>Read matrix element.</dd>
<dt id="dip-CovarianceMatrix-xy-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-CovarianceMatrix-xy-C" class="m-doc-self">xy</a>(</span><span class="m-doc-wrap">) const -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a></span>
</dt>
<dd>Read matrix element.</dd>
<dt id="dip-CovarianceMatrix-yy-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-CovarianceMatrix-yy-C" class="m-doc-self">yy</a>(</span><span class="m-doc-wrap">) const -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a></span>
</dt>
<dd>Read matrix element.</dd>
<dt id="dip-CovarianceMatrix-Det-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-CovarianceMatrix-Det-C" class="m-doc-self">Det</a>(</span><span class="m-doc-wrap">) const -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a></span>
</dt>
<dd>Compute determinant of matrix.</dd>
<dt id="dip-CovarianceMatrix-Inv-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-CovarianceMatrix-Inv-C" class="m-doc-self">Inv</a>(</span><span class="m-doc-wrap">) const -> <a href="dip-CovarianceMatrix.html" class="m-doc">dip::CovarianceMatrix</a></span>
</dt>
<dd>Compute inverse of matrix.</dd>
<dt id="dip-CovarianceMatrix-Project-VertexFloat-CL-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-CovarianceMatrix-Project-VertexFloat-CL-C" class="m-doc-self">Project</a>(</span><span class="m-doc-wrap"><a href="dip-Vertex-T.html#dip-VertexFloat" class="m-doc">dip::VertexFloat</a> const& v) const -> <a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a></span>
</dt>
<dd>Computes v’ * C * v, with v’ the transpose of v.
This is a positive scalar if v is non-zero, because C (this matrix) is positive semidefinite.</dd>
<dt id="dip-CovarianceMatrix-Eig-C">
<span class="m-doc-wrap-bumper">auto <a href="#dip-CovarianceMatrix-Eig-C" class="m-doc-self">Eig</a>(</span><span class="m-doc-wrap">) const -> <a href="dip-CovarianceMatrix-Eigenvalues.html" class="m-doc">dip::CovarianceMatrix::Eigenvalues</a></span>
</dt>
<dd>Compute eigenvalues of matrix.</dd>
<dt>
<span class="m-doc-wrap-bumper">auto <a href="#dip-CovarianceMatrix-Ellipse-bool--C" class="m-doc">Ellipse</a>(</span><span class="m-doc-wrap">bool solid = false) const -> <a href="dip-CovarianceMatrix.html#dip-CovarianceMatrix-EllipseParameters" class="m-doc">dip::CovarianceMatrix::EllipseParameters</a></span>
</dt>
<dd>Compute parameters of ellipse with same covariance matrix. <a href="#dip-CovarianceMatrix-Ellipse-bool--C">more...</a></dd>
</dl>
</section>
<section id="operator-members">
<h2>Operators</h2>
<dl class="m-doc">
<dt id="dip-CovarianceMatrix-operator%2B%3D-CovarianceMatrix-CL">
<span class="m-doc-wrap-bumper">auto <a href="#dip-CovarianceMatrix-operator%2B%3D-CovarianceMatrix-CL" class="m-doc-self">operator+=</a>(</span><span class="m-doc-wrap"><a href="dip-CovarianceMatrix.html" class="m-doc">dip::CovarianceMatrix</a> const& other) -> <a href="dip-CovarianceMatrix.html" class="m-doc">dip::CovarianceMatrix</a>&</span>
</dt>
<dd>Add other matrix to this matrix.</dd>
<dt id="dip-CovarianceMatrix-operator%2A%3D-dfloat-">
<span class="m-doc-wrap-bumper">auto <a href="#dip-CovarianceMatrix-operator%2A%3D-dfloat-" class="m-doc-self">operator*=</a>(</span><span class="m-doc-wrap"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> d) -> <a href="dip-CovarianceMatrix.html" class="m-doc">dip::CovarianceMatrix</a>&</span>
</dt>
<dd>Scale matrix.</dd>
<dt id="dip-CovarianceMatrix-operator%2F%3D-dfloat-">
<span class="m-doc-wrap-bumper">auto <a href="#dip-CovarianceMatrix-operator%2F%3D-dfloat-" class="m-doc-self">operator/=</a>(</span><span class="m-doc-wrap"><a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> d) -> <a href="dip-CovarianceMatrix.html" class="m-doc">dip::CovarianceMatrix</a>&</span>
</dt>
<dd>Scale matrix.</dd>
</dl>
</section>
<section>
<h2>Class documentation</h2>
<section class="m-doc-details" id="dip-CovarianceMatrix-EllipseParameters"><div>
<h3>
struct <a href="#dip-CovarianceMatrix-EllipseParameters" class="m-doc-self">EllipseParameters</a>
</h3>
<p>Container for ellipse parameters.</p>
<table class="m-table m-fullwidth m-first-tight m-flat m-doc">
<thead><tr><th>Variables</th><th></th></tr></thead>
<tbody>
<tr>
<td>
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> <a href="#dip-CovarianceMatrix-EllipseParameters-majorAxis" class="m-doc-self" id="dip-CovarianceMatrix-EllipseParameters-majorAxis">majorAxis</a> </td>
<td>
Major axis length
</td>
</tr>
<tr>
<td>
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> <a href="#dip-CovarianceMatrix-EllipseParameters-minorAxis" class="m-doc-self" id="dip-CovarianceMatrix-EllipseParameters-minorAxis">minorAxis</a> </td>
<td>
Minor axis length
</td>
</tr>
<tr>
<td>
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> <a href="#dip-CovarianceMatrix-EllipseParameters-orientation" class="m-doc-self" id="dip-CovarianceMatrix-EllipseParameters-orientation">orientation</a> </td>
<td>
Orientation of major axis
</td>
</tr>
<tr>
<td>
<a href="pixeltypes.html#dip-dfloat" class="m-doc">dip::dfloat</a> <a href="#dip-CovarianceMatrix-EllipseParameters-eccentricity" class="m-doc-self" id="dip-CovarianceMatrix-EllipseParameters-eccentricity">eccentricity</a> </td>
<td>
Ellipse eccentricity
</td>
</tr>
</tbody>
</table>
</div></section>
</section>
<section>
<h2>Function documentation</h2>
<section class="m-doc-details" id="dip-CovarianceMatrix-Ellipse-bool--C"><div>
<h3>
<span class="m-doc-wrap-bumper"><a href="dip-CovarianceMatrix.html#dip-CovarianceMatrix-EllipseParameters" class="m-doc">dip::CovarianceMatrix::EllipseParameters</a>
</span><span class="m-doc-wrap"><span class="m-doc-wrap-bumper"><a href="#dip-CovarianceMatrix-Ellipse-bool--C" class="m-doc-self">Ellipse</a>(</span><span class="m-doc-wrap">bool solid = false) const</span></span>
</h3>
<p>Compute parameters of ellipse with same covariance matrix.</p>
<p>If <code>solid</code> is <code>false</code> (default), then it is assumed that the covariance matrix corresponds to an ellipse
shell (e.g. obtained through <a href="dip-Polygon.html#dip-Polygon-CovarianceMatrixVertices-VertexFloat-CL-C"><code>dip::Polygon::CovarianceMatrixVertices</code></a>). This is the default for
backwards-compatibility. If <code>true</code>, the covariance matrix corresponds to a solid ellipse (e.g. obtained
though <a href="dip-Polygon.html#dip-Polygon-CovarianceMatrixSolid-VertexFloat-CL-C"><code>dip::Polygon::CovarianceMatrixSolid</code></a>).</p>
</div></section>
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