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    66. 

  66. <a href="#func-members">Functions</a>  </div>
    67. 

  67.   <div class="headertitle">
    68. 

  68. <div class="title">GLM_GTX_pca<div class="ingroups"><a class="el" href="a00905.html">Experimental extensions</a></div></div>  </div>
    69. 

  69. </div><!--header-->
    70. 

  70. <div class="contents">
    71. 

  71. <table class="memberdecls">
    72. 

  72. <tr class="heading"><td colspan="2"><h2 class="groupheader"><a name="func-members"></a>
    73. 

  73. Functions</h2></td></tr>
    74. 

  74. <tr class="memitem:ga2c7b5ff4e0f4132a23e58eeb0803b53a"><td class="memTemplParams" colspan="2"><a id="ga2c7b5ff4e0f4132a23e58eeb0803b53a"></a>
    75. 

  75. template&lt;length_t D, typename T , qualifier Q, typename I &gt; </td></tr>
    76. 

  76. <tr class="memitem:ga2c7b5ff4e0f4132a23e58eeb0803b53a"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL mat&lt; D, D, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00968.html#ga2c7b5ff4e0f4132a23e58eeb0803b53a">computeCovarianceMatrix</a> (I const &amp;b, I const &amp;e)</td></tr>
    77. 

  77. <tr class="memdesc:ga2c7b5ff4e0f4132a23e58eeb0803b53a"><td class="mdescLeft">&#160;</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&lt;D, T, Qgt;</code> <br /></td></tr>
    78. 

  78. <tr class="separator:ga2c7b5ff4e0f4132a23e58eeb0803b53a"><td class="memSeparator" colspan="2">&#160;</td></tr>
    79. 

  79. <tr class="memitem:ga666383aa52036f00f3b66e4e7e56da3a"><td class="memTemplParams" colspan="2"><a id="ga666383aa52036f00f3b66e4e7e56da3a"></a>
    80. 

  80. template&lt;length_t D, typename T , qualifier Q, typename I &gt; </td></tr>
    81. 

  81. <tr class="memitem:ga666383aa52036f00f3b66e4e7e56da3a"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL mat&lt; D, D, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00968.html#ga666383aa52036f00f3b66e4e7e56da3a">computeCovarianceMatrix</a> (I const &amp;b, I const &amp;e, vec&lt; D, T, Q &gt; const &amp;c)</td></tr>
    82. 

  82. <tr class="memdesc:ga666383aa52036f00f3b66e4e7e56da3a"><td class="mdescLeft">&#160;</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&lt;D, T, Qgt;</code> <br /></td></tr>
    83. 

  83. <tr class="separator:ga666383aa52036f00f3b66e4e7e56da3a"><td class="memSeparator" colspan="2">&#160;</td></tr>
    84. 

  84. <tr class="memitem:ga2d6dc3e25182cae243cdf55310059af0"><td class="memTemplParams" colspan="2">template&lt;length_t D, typename T , qualifier Q&gt; </td></tr>
    85. 

  85. <tr class="memitem:ga2d6dc3e25182cae243cdf55310059af0"><td class="memTemplItemLeft" align="right" valign="top">GLM_INLINE mat&lt; D, D, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00968.html#ga2d6dc3e25182cae243cdf55310059af0">computeCovarianceMatrix</a> (vec&lt; D, T, Q &gt; const *v, size_t n)</td></tr>
    86. 

  86. <tr class="memdesc:ga2d6dc3e25182cae243cdf55310059af0"><td class="mdescLeft">&#160;</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="a00968.html#ga2d6dc3e25182cae243cdf55310059af0">More...</a><br /></td></tr>
    87. 

  87. <tr class="separator:ga2d6dc3e25182cae243cdf55310059af0"><td class="memSeparator" colspan="2">&#160;</td></tr>
    88. 

  88. <tr class="memitem:gabfc7aba26da1eed6726f2484584f4077"><td class="memTemplParams" colspan="2">template&lt;length_t D, typename T , qualifier Q&gt; </td></tr>
    89. 

  89. <tr class="memitem:gabfc7aba26da1eed6726f2484584f4077"><td class="memTemplItemLeft" align="right" valign="top">GLM_INLINE mat&lt; D, D, T, Q &gt;&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00968.html#gabfc7aba26da1eed6726f2484584f4077">computeCovarianceMatrix</a> (vec&lt; D, T, Q &gt; const *v, size_t n, vec&lt; D, T, Q &gt; const &amp;c)</td></tr>
    90. 

  90. <tr class="memdesc:gabfc7aba26da1eed6726f2484584f4077"><td class="mdescLeft">&#160;</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="a00968.html#gabfc7aba26da1eed6726f2484584f4077">More...</a><br /></td></tr>
    91. 

  91. <tr class="separator:gabfc7aba26da1eed6726f2484584f4077"><td class="memSeparator" colspan="2">&#160;</td></tr>
    92. 

  92. <tr class="memitem:ga0586007af1073c8b0f629bca0ee7c46c"><td class="memTemplParams" colspan="2">template&lt;length_t D, typename T , qualifier Q&gt; </td></tr>
    93. 

  93. <tr class="memitem:ga0586007af1073c8b0f629bca0ee7c46c"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DECL unsigned int&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00968.html#ga0586007af1073c8b0f629bca0ee7c46c">findEigenvaluesSymReal</a> (mat&lt; D, D, T, Q &gt; const &amp;covarMat, vec&lt; D, T, Q &gt; &amp;outEigenvalues, mat&lt; D, D, T, Q &gt; &amp;outEigenvectors)</td></tr>
    94. 

  94. <tr class="memdesc:ga0586007af1073c8b0f629bca0ee7c46c"><td class="mdescLeft">&#160;</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="a00968.html#ga0586007af1073c8b0f629bca0ee7c46c">More...</a><br /></td></tr>
    95. 

  95. <tr class="separator:ga0586007af1073c8b0f629bca0ee7c46c"><td class="memSeparator" colspan="2">&#160;</td></tr>
    96. 

  96. <tr class="memitem:ga2824ef6f23df255f86b9c33cebd5da2f"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    97. 

  97. <tr class="memitem:ga2824ef6f23df255f86b9c33cebd5da2f"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DISCARD_DECL void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00968.html#ga2824ef6f23df255f86b9c33cebd5da2f">sortEigenvalues</a> (vec&lt; 2, T, Q &gt; &amp;eigenvalues, mat&lt; 2, 2, T, Q &gt; &amp;eigenvectors)</td></tr>
    98. 

  98. <tr class="memdesc:ga2824ef6f23df255f86b9c33cebd5da2f"><td class="mdescLeft">&#160;</td><td class="mdescRight">Sorts a group of Eigenvalues&amp;Eigenvectors, for largest Eigenvalue to smallest Eigenvalue.  <a href="a00968.html#ga2824ef6f23df255f86b9c33cebd5da2f">More...</a><br /></td></tr>
    99. 

  99. <tr class="separator:ga2824ef6f23df255f86b9c33cebd5da2f"><td class="memSeparator" colspan="2">&#160;</td></tr>
    100. 

  100. <tr class="memitem:gaf6fbcbcca3eb46f4fd6d491a979db7c5"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    101. 

  101. <tr class="memitem:gaf6fbcbcca3eb46f4fd6d491a979db7c5"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DISCARD_DECL void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00968.html#gaf6fbcbcca3eb46f4fd6d491a979db7c5">sortEigenvalues</a> (vec&lt; 3, T, Q &gt; &amp;eigenvalues, mat&lt; 3, 3, T, Q &gt; &amp;eigenvectors)</td></tr>
    102. 

  102. <tr class="memdesc:gaf6fbcbcca3eb46f4fd6d491a979db7c5"><td class="mdescLeft">&#160;</td><td class="mdescRight">Sorts a group of Eigenvalues&amp;Eigenvectors, for largest Eigenvalue to smallest Eigenvalue.  <a href="a00968.html#gaf6fbcbcca3eb46f4fd6d491a979db7c5">More...</a><br /></td></tr>
    103. 

  103. <tr class="separator:gaf6fbcbcca3eb46f4fd6d491a979db7c5"><td class="memSeparator" colspan="2">&#160;</td></tr>
    104. 

  104. <tr class="memitem:ga3fe570b4abe7eca8afb32896d77394f5"><td class="memTemplParams" colspan="2">template&lt;typename T , qualifier Q&gt; </td></tr>
    105. 

  105. <tr class="memitem:ga3fe570b4abe7eca8afb32896d77394f5"><td class="memTemplItemLeft" align="right" valign="top">GLM_FUNC_DISCARD_DECL void&#160;</td><td class="memTemplItemRight" valign="bottom"><a class="el" href="a00968.html#ga3fe570b4abe7eca8afb32896d77394f5">sortEigenvalues</a> (vec&lt; 4, T, Q &gt; &amp;eigenvalues, mat&lt; 4, 4, T, Q &gt; &amp;eigenvectors)</td></tr>
    106. 

  106. <tr class="memdesc:ga3fe570b4abe7eca8afb32896d77394f5"><td class="mdescLeft">&#160;</td><td class="mdescRight">Sorts a group of Eigenvalues&amp;Eigenvectors, for largest Eigenvalue to smallest Eigenvalue.  <a href="a00968.html#ga3fe570b4abe7eca8afb32896d77394f5">More...</a><br /></td></tr>
    107. 

  107. <tr class="separator:ga3fe570b4abe7eca8afb32896d77394f5"><td class="memSeparator" colspan="2">&#160;</td></tr>
    108. 

  108. </table>
    109. 

  109. <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
    110. 

  110. <p>Include &lt;<a class="el" href="a00704.html" title="GLM_GTX_pca">glm/gtx/pca.hpp</a>&gt; to use the features of this extension.</p>
    111. 

  111. <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>
    112. 

  112. <p>Example: </p><div class="fragment"><div class="line">std::vector&lt;glm::dvec3&gt; ptData;</div>
    113. 

  113. <div class="line"><span class="comment">// ... fill ptData with some point data, e.g. vertices</span></div>
    114. 

  114. <div class="line"> </div>
    115. 

  115. <div class="line"><a class="code" href="a00899.html#ga5b83ae3d0fdec519c038e4d2cf967cf0">glm::dvec3</a> center = computeCenter(ptData);</div>
    116. 

  116. <div class="line"> </div>
    117. 

  117. <div class="line"><a class="code" href="a00901.html#ga6f40aa56265b4b0ccad41b86802efe33">glm::dmat3</a> covarMat = <a class="code" href="a00968.html#ga2d6dc3e25182cae243cdf55310059af0">glm::computeCovarianceMatrix</a>(ptData.data(), ptData.size(), center);</div>
    118. 

  118. <div class="line"> </div>
    119. 

  119. <div class="line"><a class="code" href="a00899.html#ga5b83ae3d0fdec519c038e4d2cf967cf0">glm::dvec3</a> evals;</div>
    120. 

  120. <div class="line"><a class="code" href="a00901.html#ga6f40aa56265b4b0ccad41b86802efe33">glm::dmat3</a> evecs;</div>
    121. 

  121. <div class="line"><span class="keywordtype">int</span> evcnt = <a class="code" href="a00968.html#ga0586007af1073c8b0f629bca0ee7c46c">glm::findEigenvaluesSymReal</a>(covarMat, evals, evecs);</div>
    122. 

  122. <div class="line"> </div>
    123. 

  123. <div class="line"><span class="keywordflow">if</span>(evcnt != 3)</div>
    124. 

  124. <div class="line">    <span class="comment">// ... error handling</span></div>
    125. 

  125. <div class="line"> </div>
    126. 

  126. <div class="line"><a class="code" href="a00968.html#ga2824ef6f23df255f86b9c33cebd5da2f">glm::sortEigenvalues</a>(evals, evecs);</div>
    127. 

  127. <div class="line"> </div>
    128. 

  128. <div class="line"><span class="comment">// ... now evecs[0] points in the direction (symmetric) of the largest spatial distribution within ptData</span></div>
    129. 

  129. </div><!-- fragment --> <h2 class="groupheader">Function Documentation</h2>
    130. 

  130. <a id="ga2d6dc3e25182cae243cdf55310059af0"></a>
    131. 

  131. <h2 class="memtitle"><span class="permalink"><a href="#ga2d6dc3e25182cae243cdf55310059af0">&#9670;&nbsp;</a></span>computeCovarianceMatrix() <span class="overload">[1/2]</span></h2>
    132. 

  132. 

  133. <div class="memitem">
    134. 

  134. <div class="memproto">
    135. 

  135.       <table class="memname">
    136. 

  136.         <tr>
    137. 

  137.           <td class="memname">GLM_INLINE mat&lt;D, D, T, Q&gt; glm::computeCovarianceMatrix </td>
    138. 

  138.           <td>(</td>
    139. 

  139.           <td class="paramtype">vec&lt; D, T, Q &gt; const *&#160;</td>
    140. 

  140.           <td class="paramname"><em>v</em>, </td>
    141. 

  141.         </tr>
    142. 

  142.         <tr>
    143. 

  143.           <td class="paramkey"></td>
    144. 

  144.           <td></td>
    145. 

  145.           <td class="paramtype">size_t&#160;</td>
    146. 

  146.           <td class="paramname"><em>n</em>&#160;</td>
    147. 

  147.         </tr>
    148. 

  148.         <tr>
    149. 

  149.           <td></td>
    150. 

  150.           <td>)</td>
    151. 

  151.           <td></td><td></td>
    152. 

  152.         </tr>
    153. 

  153.       </table>
    154. 

  154. </div><div class="memdoc">
    155. 

  155. 

  156. <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>
    157. 

  157. <dl class="params"><dt>Parameters</dt><dd>
    158. 

  158.   <table class="params">
    159. 

  159.     <tr><td class="paramname">v</td><td>Points to a memory holding <code>n</code> times vectors </td></tr>
    160. 

  160.     <tr><td class="paramname">n</td><td>Number of points in v </td></tr>
    161. 

  161.   </table>
    162. 

  162.   </dd>
    163. 

  163. </dl>
    164. 

  164. 

  165. </div>
    166. 

  166. </div>
    167. 

  167. <a id="gabfc7aba26da1eed6726f2484584f4077"></a>
    168. 

  168. <h2 class="memtitle"><span class="permalink"><a href="#gabfc7aba26da1eed6726f2484584f4077">&#9670;&nbsp;</a></span>computeCovarianceMatrix() <span class="overload">[2/2]</span></h2>
    169. 

  169. 

  170. <div class="memitem">
    171. 

  171. <div class="memproto">
    172. 

  172.       <table class="memname">
    173. 

  173.         <tr>
    174. 

  174.           <td class="memname">GLM_INLINE mat&lt;D, D, T, Q&gt; glm::computeCovarianceMatrix </td>
    175. 

  175.           <td>(</td>
    176. 

  176.           <td class="paramtype">vec&lt; D, T, Q &gt; const *&#160;</td>
    177. 

  177.           <td class="paramname"><em>v</em>, </td>
    178. 

  178.         </tr>
    179. 

  179.         <tr>
    180. 

  180.           <td class="paramkey"></td>
    181. 

  181.           <td></td>
    182. 

  182.           <td class="paramtype">size_t&#160;</td>
    183. 

  183.           <td class="paramname"><em>n</em>, </td>
    184. 

  184.         </tr>
    185. 

  185.         <tr>
    186. 

  186.           <td class="paramkey"></td>
    187. 

  187.           <td></td>
    188. 

  188.           <td class="paramtype">vec&lt; D, T, Q &gt; const &amp;&#160;</td>
    189. 

  189.           <td class="paramname"><em>c</em>&#160;</td>
    190. 

  190.         </tr>
    191. 

  191.         <tr>
    192. 

  192.           <td></td>
    193. 

  193.           <td>)</td>
    194. 

  194.           <td></td><td></td>
    195. 

  195.         </tr>
    196. 

  196.       </table>
    197. 

  197. </div><div class="memdoc">
    198. 

  198. 

  199. <p>Compute a covariance matrix form an array of absolute coordinates <code>v</code> and a precomputed center of gravity <code>c</code> </p>
    200. 

  200. <dl class="params"><dt>Parameters</dt><dd>
    201. 

  201.   <table class="params">
    202. 

  202.     <tr><td class="paramname">v</td><td>Points to a memory holding <code>n</code> times vectors </td></tr>
    203. 

  203.     <tr><td class="paramname">n</td><td>Number of points in v </td></tr>
    204. 

  204.     <tr><td class="paramname">c</td><td>Precomputed center of gravity </td></tr>
    205. 

  205.   </table>
    206. 

  206.   </dd>
    207. 

  207. </dl>
    208. 

  208. 

  209. </div>
    210. 

  210. </div>
    211. 

  211. <a id="ga0586007af1073c8b0f629bca0ee7c46c"></a>
    212. 

  212. <h2 class="memtitle"><span class="permalink"><a href="#ga0586007af1073c8b0f629bca0ee7c46c">&#9670;&nbsp;</a></span>findEigenvaluesSymReal()</h2>
    213. 

  213. 

  214. <div class="memitem">
    215. 

  215. <div class="memproto">
    216. 

  216.       <table class="memname">
    217. 

  217.         <tr>
    218. 

  218.           <td class="memname">GLM_FUNC_DECL unsigned int glm::findEigenvaluesSymReal </td>
    219. 

  219.           <td>(</td>
    220. 

  220.           <td class="paramtype">mat&lt; D, D, T, Q &gt; const &amp;&#160;</td>
    221. 

  221.           <td class="paramname"><em>covarMat</em>, </td>
    222. 

  222.         </tr>
    223. 

  223.         <tr>
    224. 

  224.           <td class="paramkey"></td>
    225. 

  225.           <td></td>
    226. 

  226.           <td class="paramtype">vec&lt; D, T, Q &gt; &amp;&#160;</td>
    227. 

  227.           <td class="paramname"><em>outEigenvalues</em>, </td>
    228. 

  228.         </tr>
    229. 

  229.         <tr>
    230. 

  230.           <td class="paramkey"></td>
    231. 

  231.           <td></td>
    232. 

  232.           <td class="paramtype">mat&lt; D, D, T, Q &gt; &amp;&#160;</td>
    233. 

  233.           <td class="paramname"><em>outEigenvectors</em>&#160;</td>
    234. 

  234.         </tr>
    235. 

  235.         <tr>
    236. 

  236.           <td></td>
    237. 

  237.           <td>)</td>
    238. 

  238.           <td></td><td></td>
    239. 

  239.         </tr>
    240. 

  240.       </table>
    241. 

  241. </div><div class="memdoc">
    242. 

  242. 

  243. <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>
    244. 

  244. <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>
    245. 

  245. <dl class="params"><dt>Parameters</dt><dd>
    246. 

  246.   <table class="params">
    247. 

  247.     <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>
    248. 

  248.     <tr><td class="paramdir">[out]</td><td class="paramname">outEigenvalues</td><td>Vector to receive the found eigenvalues </td></tr>
    249. 

  249.     <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>
    250. 

  250.   </table>
    251. 

  251.   </dd>
    252. 

  252. </dl>
    253. 

  253. <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>
    254. 

  254. 

  255. </div>
    256. 

  256. </div>
    257. 

  257. <a id="ga2824ef6f23df255f86b9c33cebd5da2f"></a>
    258. 

  258. <h2 class="memtitle"><span class="permalink"><a href="#ga2824ef6f23df255f86b9c33cebd5da2f">&#9670;&nbsp;</a></span>sortEigenvalues() <span class="overload">[1/3]</span></h2>
    259. 

  259. 

  260. <div class="memitem">
    261. 

  261. <div class="memproto">
    262. 

  262.       <table class="memname">
    263. 

  263.         <tr>
    264. 

  264.           <td class="memname">GLM_FUNC_DISCARD_DECL void glm::sortEigenvalues </td>
    265. 

  265.           <td>(</td>
    266. 

  266.           <td class="paramtype">vec&lt; 2, T, Q &gt; &amp;&#160;</td>
    267. 

  267.           <td class="paramname"><em>eigenvalues</em>, </td>
    268. 

  268.         </tr>
    269. 

  269.         <tr>
    270. 

  270.           <td class="paramkey"></td>
    271. 

  271.           <td></td>
    272. 

  272.           <td class="paramtype">mat&lt; 2, 2, T, Q &gt; &amp;&#160;</td>
    273. 

  273.           <td class="paramname"><em>eigenvectors</em>&#160;</td>
    274. 

  274.         </tr>
    275. 

  275.         <tr>
    276. 

  276.           <td></td>
    277. 

  277.           <td>)</td>
    278. 

  278.           <td></td><td></td>
    279. 

  279.         </tr>
    280. 

  280.       </table>
    281. 

  281. </div><div class="memdoc">
    282. 

  282. 

  283. <p>Sorts a group of Eigenvalues&amp;Eigenvectors, for largest Eigenvalue to smallest Eigenvalue. </p>
    284. 

  284. <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>
    285. 

  285. 

  286. </div>
    287. 

  287. </div>
    288. 

  288. <a id="gaf6fbcbcca3eb46f4fd6d491a979db7c5"></a>
    289. 

  289. <h2 class="memtitle"><span class="permalink"><a href="#gaf6fbcbcca3eb46f4fd6d491a979db7c5">&#9670;&nbsp;</a></span>sortEigenvalues() <span class="overload">[2/3]</span></h2>
    290. 

  290. 

  291. <div class="memitem">
    292. 

  292. <div class="memproto">
    293. 

  293.       <table class="memname">
    294. 

  294.         <tr>
    295. 

  295.           <td class="memname">GLM_FUNC_DISCARD_DECL void glm::sortEigenvalues </td>
    296. 

  296.           <td>(</td>
    297. 

  297.           <td class="paramtype">vec&lt; 3, T, Q &gt; &amp;&#160;</td>
    298. 

  298.           <td class="paramname"><em>eigenvalues</em>, </td>
    299. 

  299.         </tr>
    300. 

  300.         <tr>
    301. 

  301.           <td class="paramkey"></td>
    302. 

  302.           <td></td>
    303. 

  303.           <td class="paramtype">mat&lt; 3, 3, T, Q &gt; &amp;&#160;</td>
    304. 

  304.           <td class="paramname"><em>eigenvectors</em>&#160;</td>
    305. 

  305.         </tr>
    306. 

  306.         <tr>
    307. 

  307.           <td></td>
    308. 

  308.           <td>)</td>
    309. 

  309.           <td></td><td></td>
    310. 

  310.         </tr>
    311. 

  311.       </table>
    312. 

  312. </div><div class="memdoc">
    313. 

  313. 

  314. <p>Sorts a group of Eigenvalues&amp;Eigenvectors, for largest Eigenvalue to smallest Eigenvalue. </p>
    315. 

  315. <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>
    316. 

  316. 

  317. </div>
    318. 

  318. </div>
    319. 

  319. <a id="ga3fe570b4abe7eca8afb32896d77394f5"></a>
    320. 

  320. <h2 class="memtitle"><span class="permalink"><a href="#ga3fe570b4abe7eca8afb32896d77394f5">&#9670;&nbsp;</a></span>sortEigenvalues() <span class="overload">[3/3]</span></h2>
    321. 

  321. 

  322. <div class="memitem">
    323. 

  323. <div class="memproto">
    324. 

  324.       <table class="memname">
    325. 

  325.         <tr>
    326. 

  326.           <td class="memname">GLM_FUNC_DISCARD_DECL void glm::sortEigenvalues </td>
    327. 

  327.           <td>(</td>
    328. 

  328.           <td class="paramtype">vec&lt; 4, T, Q &gt; &amp;&#160;</td>
    329. 

  329.           <td class="paramname"><em>eigenvalues</em>, </td>
    330. 

  330.         </tr>
    331. 

  331.         <tr>
    332. 

  332.           <td class="paramkey"></td>
    333. 

  333.           <td></td>
    334. 

  334.           <td class="paramtype">mat&lt; 4, 4, T, Q &gt; &amp;&#160;</td>
    335. 

  335.           <td class="paramname"><em>eigenvectors</em>&#160;</td>
    336. 

  336.         </tr>
    337. 

  337.         <tr>
    338. 

  338.           <td></td>
    339. 

  339.           <td>)</td>
    340. 

  340.           <td></td><td></td>
    341. 

  341.         </tr>
    342. 

  342.       </table>
    343. 

  343. </div><div class="memdoc">
    344. 

  344. 

  345. <p>Sorts a group of Eigenvalues&amp;Eigenvectors, for largest Eigenvalue to smallest Eigenvalue. </p>
    346. 

  346. <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>
    347. 

  347. 

  348. </div>
    349. 

  349. </div>
    350. 

  350. </div><!-- contents -->
    351. 

  351. <div class="ttc" id="aa00968_html_ga2824ef6f23df255f86b9c33cebd5da2f"><div class="ttname"><a href="a00968.html#ga2824ef6f23df255f86b9c33cebd5da2f">glm::sortEigenvalues</a></div><div class="ttdeci">GLM_FUNC_DISCARD_DECL void sortEigenvalues(vec&lt; 2, T, Q &gt; &amp;eigenvalues, mat&lt; 2, 2, T, Q &gt; &amp;eigenvectors)</div><div class="ttdoc">Sorts a group of Eigenvalues&amp;Eigenvectors, for largest Eigenvalue to smallest Eigenvalue.</div></div>
    352. 

  352. <div class="ttc" id="aa00968_html_ga2d6dc3e25182cae243cdf55310059af0"><div class="ttname"><a href="a00968.html#ga2d6dc3e25182cae243cdf55310059af0">glm::computeCovarianceMatrix</a></div><div class="ttdeci">GLM_INLINE mat&lt; D, D, T, Q &gt; computeCovarianceMatrix(vec&lt; D, T, Q &gt; 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>
    353. 

  353. <div class="ttc" id="aa00899_html_ga5b83ae3d0fdec519c038e4d2cf967cf0"><div class="ttname"><a href="a00899.html#ga5b83ae3d0fdec519c038e4d2cf967cf0">glm::dvec3</a></div><div class="ttdeci">vec&lt; 3, double, defaultp &gt; dvec3</div><div class="ttdoc">3 components vector of double-precision floating-point numbers.</div><div class="ttdef"><b>Definition:</b> <a href="a00422_source.html#l00015">vector_double3.hpp:15</a></div></div>
    354. 

  354. <div class="ttc" id="aa00901_html_ga6f40aa56265b4b0ccad41b86802efe33"><div class="ttname"><a href="a00901.html#ga6f40aa56265b4b0ccad41b86802efe33">glm::dmat3</a></div><div class="ttdeci">mat&lt; 3, 3, double, defaultp &gt; 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="a00122_source.html#l00020">matrix_double3x3.hpp:20</a></div></div>
    355. 

  355. <div class="ttc" id="aa00968_html_ga0586007af1073c8b0f629bca0ee7c46c"><div class="ttname"><a href="a00968.html#ga0586007af1073c8b0f629bca0ee7c46c">glm::findEigenvaluesSymReal</a></div><div class="ttdeci">GLM_FUNC_DECL unsigned int findEigenvaluesSymReal(mat&lt; D, D, T, Q &gt; const &amp;covarMat, vec&lt; D, T, Q &gt; &amp;outEigenvalues, mat&lt; D, D, T, Q &gt; &amp;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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