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<a href="#func-members">Functions</a> </div>
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<div class="title">GLM_GTX_pca<div class="ingroups"><a class="el" href="a00896.html">Experimental extensions</a></div></div> </div>
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<table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:ga2c7b5ff4e0f4132a23e58eeb0803b53a"><td class="memTemplParams" colspan="2"><a id="ga2c7b5ff4e0f4132a23e58eeb0803b53a"></a>
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template<length_t D, typename T , qualifier Q, typename I > </td></tr>
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<tr class="memitem:ga2c7b5ff4e0f4132a23e58eeb0803b53a"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL mat< D, D, T, Q > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00958.html#ga2c7b5ff4e0f4132a23e58eeb0803b53a">computeCovarianceMatrix</a> (I const &b, I const &e)</td></tr>
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<tr class="memdesc:ga2c7b5ff4e0f4132a23e58eeb0803b53a"><td class="mdescLeft"> </td><td class="mdescRight">Compute a covariance matrix form a pair of iterators <code>b</code> (begin) and <code>e</code> (end) of a container with relative coordinates (e.g., relative to the center of gravity of the object) Dereferencing an iterator of type I must yield a <code>vec<D, T, Qgt;</code> <br /></td></tr>
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<tr class="separator:ga2c7b5ff4e0f4132a23e58eeb0803b53a"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga666383aa52036f00f3b66e4e7e56da3a"><td class="memTemplParams" colspan="2"><a id="ga666383aa52036f00f3b66e4e7e56da3a"></a>
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template<length_t D, typename T , qualifier Q, typename I > </td></tr>
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<tr class="memitem:ga666383aa52036f00f3b66e4e7e56da3a"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL mat< D, D, T, Q > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00958.html#ga666383aa52036f00f3b66e4e7e56da3a">computeCovarianceMatrix</a> (I const &b, I const &e, vec< D, T, Q > const &c)</td></tr>
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<tr class="memdesc:ga666383aa52036f00f3b66e4e7e56da3a"><td class="mdescLeft"> </td><td class="mdescRight">Compute a covariance matrix form a pair of iterators <code>b</code> (begin) and <code>e</code> (end) of a container with absolute coordinates and a precomputed center of gravity <code>c</code> Dereferencing an iterator of type I must yield a <code>vec<D, T, Qgt;</code> <br /></td></tr>
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<tr class="separator:ga666383aa52036f00f3b66e4e7e56da3a"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga2d6dc3e25182cae243cdf55310059af0"><td class="memTemplParams" colspan="2">template<length_t D, typename T , qualifier Q> </td></tr>
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<tr class="memitem:ga2d6dc3e25182cae243cdf55310059af0"><td class="memTemplItemLeft" align="right" valign="top">GLM_INLINE mat< D, D, T, Q > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00958.html#ga2d6dc3e25182cae243cdf55310059af0">computeCovarianceMatrix</a> (vec< D, T, Q > const *v, size_t n)</td></tr>
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<tr class="memdesc:ga2d6dc3e25182cae243cdf55310059af0"><td class="mdescLeft"> </td><td class="mdescRight">Compute a covariance matrix form an array of relative coordinates <code>v</code> (e.g., relative to the center of gravity of the object) <a href="a00958.html#ga2d6dc3e25182cae243cdf55310059af0">More...</a><br /></td></tr>
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<tr class="separator:ga2d6dc3e25182cae243cdf55310059af0"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:gabfc7aba26da1eed6726f2484584f4077"><td class="memTemplParams" colspan="2">template<length_t D, typename T , qualifier Q> </td></tr>
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<tr class="memitem:gabfc7aba26da1eed6726f2484584f4077"><td class="memTemplItemLeft" align="right" valign="top">GLM_INLINE mat< D, D, T, Q > </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00958.html#gabfc7aba26da1eed6726f2484584f4077">computeCovarianceMatrix</a> (vec< D, T, Q > const *v, size_t n, vec< D, T, Q > const &c)</td></tr>
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<tr class="memdesc:gabfc7aba26da1eed6726f2484584f4077"><td class="mdescLeft"> </td><td class="mdescRight">Compute a covariance matrix form an array of absolute coordinates <code>v</code> and a precomputed center of gravity <code>c</code> <a href="a00958.html#gabfc7aba26da1eed6726f2484584f4077">More...</a><br /></td></tr>
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<tr class="separator:gabfc7aba26da1eed6726f2484584f4077"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga0586007af1073c8b0f629bca0ee7c46c"><td class="memTemplParams" colspan="2">template<length_t D, typename T , qualifier Q> </td></tr>
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<tr class="memitem:ga0586007af1073c8b0f629bca0ee7c46c"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL unsigned int </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00958.html#ga0586007af1073c8b0f629bca0ee7c46c">findEigenvaluesSymReal</a> (mat< D, D, T, Q > const &covarMat, vec< D, T, Q > &outEigenvalues, mat< D, D, T, Q > &outEigenvectors)</td></tr>
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<tr class="memdesc:ga0586007af1073c8b0f629bca0ee7c46c"><td class="mdescLeft"> </td><td class="mdescRight">Assuming the provided covariance matrix <code>covarMat</code> is symmetric and real-valued, this function find the <code>D</code> Eigenvalues of the matrix, and also provides the corresponding Eigenvectors. <a href="a00958.html#ga0586007af1073c8b0f629bca0ee7c46c">More...</a><br /></td></tr>
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<tr class="separator:ga0586007af1073c8b0f629bca0ee7c46c"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ga86e8b8630d5731bb385a979038c62258"><td class="memTemplParams" colspan="2">template<typename T , qualifier Q> </td></tr>
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<tr class="memitem:ga86e8b8630d5731bb385a979038c62258"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00958.html#ga86e8b8630d5731bb385a979038c62258">sortEigenvalues</a> (vec< 2, T, Q > &eigenvalues, mat< 2, 2, T, Q > &eigenvectors)</td></tr>
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<tr class="memdesc:ga86e8b8630d5731bb385a979038c62258"><td class="mdescLeft"> </td><td class="mdescRight">Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue. <a href="a00958.html#ga86e8b8630d5731bb385a979038c62258">More...</a><br /></td></tr>
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<tr class="separator:ga86e8b8630d5731bb385a979038c62258"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:gaafa0226e6e0d0d8c5cb47bc9466f8eac"><td class="memTemplParams" colspan="2">template<typename T , qualifier Q> </td></tr>
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<tr class="memitem:gaafa0226e6e0d0d8c5cb47bc9466f8eac"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00958.html#gaafa0226e6e0d0d8c5cb47bc9466f8eac">sortEigenvalues</a> (vec< 3, T, Q > &eigenvalues, mat< 3, 3, T, Q > &eigenvectors)</td></tr>
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<tr class="memdesc:gaafa0226e6e0d0d8c5cb47bc9466f8eac"><td class="mdescLeft"> </td><td class="mdescRight">Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue. <a href="a00958.html#gaafa0226e6e0d0d8c5cb47bc9466f8eac">More...</a><br /></td></tr>
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<tr class="separator:gaafa0226e6e0d0d8c5cb47bc9466f8eac"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:gaf23e35406e7e192520bd670b20235d5b"><td class="memTemplParams" colspan="2">template<typename T , qualifier Q> </td></tr>
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<tr class="memitem:gaf23e35406e7e192520bd670b20235d5b"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00958.html#gaf23e35406e7e192520bd670b20235d5b">sortEigenvalues</a> (vec< 4, T, Q > &eigenvalues, mat< 4, 4, T, Q > &eigenvectors)</td></tr>
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<tr class="memdesc:gaf23e35406e7e192520bd670b20235d5b"><td class="mdescLeft"> </td><td class="mdescRight">Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue. <a href="a00958.html#gaf23e35406e7e192520bd670b20235d5b">More...</a><br /></td></tr>
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<tr class="separator:gaf23e35406e7e192520bd670b20235d5b"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<p>Include <<a class="el" href="a00698.html" title="GLM_GTX_pca">glm/gtx/pca.hpp</a>> to use the features of this extension.</p>
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<p>Implements functions required for fundamental 'princple component analysis' in 2D, 3D, and 4D: 1) Computing a covariance matrics from a list of <em>relative</em> position vectors 2) Compute the eigenvalues and eigenvectors of the covariance matrics This is useful, e.g., to compute an object-aligned bounding box from vertices of an object. <a href="https://en.wikipedia.org/wiki/Principal_component_analysis">https://en.wikipedia.org/wiki/Principal_component_analysis</a></p>
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<p>Example: </p><div class="fragment"><div class="line">std::vector<glm::dvec3> ptData;</div>
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<div class="line"><span class="comment">// ... fill ptData with some point data, e.g. vertices</span></div>
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<div class="line"> </div>
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<div class="line"><a class="code" href="a00890.html#ga5b83ae3d0fdec519c038e4d2cf967cf0">glm::dvec3</a> center = computeCenter(ptData);</div>
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<div class="line"> </div>
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<div class="line"><a class="code" href="a00892.html#ga6f40aa56265b4b0ccad41b86802efe33">glm::dmat3</a> covarMat = <a class="code" href="a00958.html#ga2d6dc3e25182cae243cdf55310059af0">glm::computeCovarianceMatrix</a>(ptData.data(), ptData.size(), center);</div>
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<div class="line"> </div>
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<div class="line"><a class="code" href="a00890.html#ga5b83ae3d0fdec519c038e4d2cf967cf0">glm::dvec3</a> evals;</div>
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<div class="line"><a class="code" href="a00892.html#ga6f40aa56265b4b0ccad41b86802efe33">glm::dmat3</a> evecs;</div>
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<div class="line"><span class="keywordtype">int</span> evcnt = <a class="code" href="a00958.html#ga0586007af1073c8b0f629bca0ee7c46c">glm::findEigenvaluesSymReal</a>(covarMat, evals, evecs);</div>
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<div class="line"> </div>
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<div class="line"><span class="keywordflow">if</span>(evcnt != 3)</div>
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<div class="line"> <span class="comment">// ... error handling</span></div>
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<div class="line"> </div>
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<div class="line"><a class="code" href="a00958.html#ga86e8b8630d5731bb385a979038c62258">glm::sortEigenvalues</a>(evals, evecs);</div>
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<div class="line"> </div>
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<div class="line"><span class="comment">// ... now evecs[0] points in the direction (symmetric) of the largest spatial distribution within ptData</span></div>
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</div><!-- fragment --> <h2 class="groupheader">Function Documentation</h2>
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<a id="ga2d6dc3e25182cae243cdf55310059af0"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ga2d6dc3e25182cae243cdf55310059af0">◆ </a></span>computeCovarianceMatrix() <span class="overload">[1/2]</span></h2>
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<div class="memitem">
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<td class="memname">GLM_INLINE mat<D, D, T, Q> glm::computeCovarianceMatrix </td>
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<td>(</td>
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<td class="paramtype">vec< D, T, Q > const * </td>
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<td class="paramname"><em>v</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">size_t </td>
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<td class="paramname"><em>n</em> </td>
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<td></td>
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<td>)</td>
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</div><div class="memdoc">
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<p>Compute a covariance matrix form an array of relative coordinates <code>v</code> (e.g., relative to the center of gravity of the object) </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">v</td><td>Points to a memory holding <code>n</code> times vectors </td></tr>
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<tr><td class="paramname">n</td><td>Number of points in v </td></tr>
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</table>
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</dd>
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</dl>
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<a id="gabfc7aba26da1eed6726f2484584f4077"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#gabfc7aba26da1eed6726f2484584f4077">◆ </a></span>computeCovarianceMatrix() <span class="overload">[2/2]</span></h2>
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<td class="memname">GLM_INLINE mat<D, D, T, Q> glm::computeCovarianceMatrix </td>
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<td>(</td>
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<td class="paramtype">vec< D, T, Q > const * </td>
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<td class="paramname"><em>v</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">size_t </td>
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<td class="paramname"><em>n</em>, </td>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">vec< D, T, Q > const & </td>
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<td class="paramname"><em>c</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</table>
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</div><div class="memdoc">
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<p>Compute a covariance matrix form an array of absolute coordinates <code>v</code> and a precomputed center of gravity <code>c</code> </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">v</td><td>Points to a memory holding <code>n</code> times vectors </td></tr>
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<tr><td class="paramname">n</td><td>Number of points in v </td></tr>
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<tr><td class="paramname">c</td><td>Precomputed center of gravity </td></tr>
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</table>
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</dd>
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</dl>
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<a id="ga0586007af1073c8b0f629bca0ee7c46c"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ga0586007af1073c8b0f629bca0ee7c46c">◆ </a></span>findEigenvaluesSymReal()</h2>
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<td class="memname">GLM_FUNC_DECL unsigned int glm::findEigenvaluesSymReal </td>
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<td>(</td>
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<td class="paramtype">mat< D, D, T, Q > const & </td>
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<td class="paramname"><em>covarMat</em>, </td>
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</tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">vec< D, T, Q > & </td>
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<td class="paramname"><em>outEigenvalues</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">mat< D, D, T, Q > & </td>
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<td class="paramname"><em>outEigenvectors</em> </td>
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<tr>
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<td></td>
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<td>)</td>
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<p>Assuming the provided covariance matrix <code>covarMat</code> is symmetric and real-valued, this function find the <code>D</code> Eigenvalues of the matrix, and also provides the corresponding Eigenvectors. </p>
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<p>Note: the data in <code>outEigenvalues</code> and <code>outEigenvectors</code> are in matching order, i.e. <code>outEigenvector[i]</code> is the Eigenvector of the Eigenvalue <code>outEigenvalue[i]</code>. This is a numeric implementation to find the Eigenvalues, using 'QL decomposition` (variant of QR decomposition: <a href="https://en.wikipedia.org/wiki/QR_decomposition">https://en.wikipedia.org/wiki/QR_decomposition</a>).</p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramdir">[in]</td><td class="paramname">covarMat</td><td>A symmetric, real-valued covariance matrix, e.g. computed from computeCovarianceMatrix </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">outEigenvalues</td><td>Vector to receive the found eigenvalues </td></tr>
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<tr><td class="paramdir">[out]</td><td class="paramname">outEigenvectors</td><td>Matrix to receive the found eigenvectors corresponding to the found eigenvalues, as column vectors </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>The number of eigenvalues found, usually D if the precondition of the covariance matrix is met. </dd></dl>
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<a id="ga86e8b8630d5731bb385a979038c62258"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ga86e8b8630d5731bb385a979038c62258">◆ </a></span>sortEigenvalues() <span class="overload">[1/3]</span></h2>
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<td class="memname">GLM_FUNC_DECL void glm::sortEigenvalues </td>
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<td>(</td>
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<td class="paramtype">vec< 2, T, Q > & </td>
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<td class="paramname"><em>eigenvalues</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">mat< 2, 2, T, Q > & </td>
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<td class="paramname"><em>eigenvectors</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue. </p>
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<p>The data in <code>outEigenvalues</code> and <code>outEigenvectors</code> are assumed to be matching order, i.e. <code>outEigenvector[i]</code> is the Eigenvector of the Eigenvalue <code>outEigenvalue[i]</code>. </p>
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<a id="gaafa0226e6e0d0d8c5cb47bc9466f8eac"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#gaafa0226e6e0d0d8c5cb47bc9466f8eac">◆ </a></span>sortEigenvalues() <span class="overload">[2/3]</span></h2>
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<td class="memname">GLM_FUNC_DECL void glm::sortEigenvalues </td>
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<td>(</td>
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<td class="paramtype">vec< 3, T, Q > & </td>
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<td class="paramname"><em>eigenvalues</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">mat< 3, 3, T, Q > & </td>
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<td class="paramname"><em>eigenvectors</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue. </p>
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<p>The data in <code>outEigenvalues</code> and <code>outEigenvectors</code> are assumed to be matching order, i.e. <code>outEigenvector[i]</code> is the Eigenvector of the Eigenvalue <code>outEigenvalue[i]</code>. </p>
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</div>
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<a id="gaf23e35406e7e192520bd670b20235d5b"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#gaf23e35406e7e192520bd670b20235d5b">◆ </a></span>sortEigenvalues() <span class="overload">[3/3]</span></h2>
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<td class="memname">GLM_FUNC_DECL void glm::sortEigenvalues </td>
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<td>(</td>
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<td class="paramtype">vec< 4, T, Q > & </td>
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<td class="paramname"><em>eigenvalues</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">mat< 4, 4, T, Q > & </td>
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<td class="paramname"><em>eigenvectors</em> </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue. </p>
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<p>The data in <code>outEigenvalues</code> and <code>outEigenvectors</code> are assumed to be matching order, i.e. <code>outEigenvector[i]</code> is the Eigenvector of the Eigenvalue <code>outEigenvalue[i]</code>. </p>
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</div>
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</div><!-- contents -->
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<div class="ttc" id="aa00958_html_ga2d6dc3e25182cae243cdf55310059af0"><div class="ttname"><a href="a00958.html#ga2d6dc3e25182cae243cdf55310059af0">glm::computeCovarianceMatrix</a></div><div class="ttdeci">GLM_INLINE mat< D, D, T, Q > computeCovarianceMatrix(vec< D, T, Q > const *v, size_t n)</div><div class="ttdoc">Compute a covariance matrix form an array of relative coordinates v (e.g., relative to the center of ...</div></div>
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<div class="ttc" id="aa00958_html_ga86e8b8630d5731bb385a979038c62258"><div class="ttname"><a href="a00958.html#ga86e8b8630d5731bb385a979038c62258">glm::sortEigenvalues</a></div><div class="ttdeci">GLM_FUNC_DECL void sortEigenvalues(vec< 2, T, Q > &eigenvalues, mat< 2, 2, T, Q > &eigenvectors)</div><div class="ttdoc">Sorts a group of Eigenvalues&Eigenvectors, for largest Eigenvalue to smallest Eigenvalue.</div></div>
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<div class="ttc" id="aa00892_html_ga6f40aa56265b4b0ccad41b86802efe33"><div class="ttname"><a href="a00892.html#ga6f40aa56265b4b0ccad41b86802efe33">glm::dmat3</a></div><div class="ttdeci">mat< 3, 3, double, defaultp > dmat3</div><div class="ttdoc">3 columns of 3 components matrix of double-precision floating-point numbers.</div><div class="ttdef"><b>Definition:</b> <a href="a00119_source.html#l00020">matrix_double3x3.hpp:20</a></div></div>
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<div class="ttc" id="aa00890_html_ga5b83ae3d0fdec519c038e4d2cf967cf0"><div class="ttname"><a href="a00890.html#ga5b83ae3d0fdec519c038e4d2cf967cf0">glm::dvec3</a></div><div class="ttdeci">vec< 3, double, defaultp > dvec3</div><div class="ttdoc">3 components vector of double-precision floating-point numbers.</div><div class="ttdef"><b>Definition:</b> <a href="a00419_source.html#l00015">vector_double3.hpp:15</a></div></div>
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<div class="ttc" id="aa00958_html_ga0586007af1073c8b0f629bca0ee7c46c"><div class="ttname"><a href="a00958.html#ga0586007af1073c8b0f629bca0ee7c46c">glm::findEigenvaluesSymReal</a></div><div class="ttdeci">GLM_FUNC_DECL unsigned int findEigenvaluesSymReal(mat< D, D, T, Q > const &covarMat, vec< D, T, Q > &outEigenvalues, mat< D, D, T, Q > &outEigenvectors)</div><div class="ttdoc">Assuming the provided covariance matrix covarMat is symmetric and real-valued, this function find the...</div></div>
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