<div dir="ltr">It is the covariance of the XYZ coordinates alone.</div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Jul 8, 2019 at 12:47 PM Joseph S Faraguna <<a href="mailto:faraguna@mit.edu">faraguna@mit.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="ltr">Hi everyone,<div><br></div><div>I am wondering what matrix is passed into Eigen's <a href="https://eigen.tuxfamily.org/dox/classEigen_1_1SelfAdjointEigenSolver.html" target="_blank">SelfAdjointEigenSolver</a> when <a href="http://filters.eigenvalues" target="_blank">filters.eigenvalues</a> is called on a .las file. The filters.eigenvalues documentation states that the decomposition is performed for each point with knn nearest neighbors, but to my understanding decompositions can only be performed on square matrices. I was originally imagining a matrix of points like</div><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><div>[x0 x1 x2 x3 ... xknn]</div></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><div>]y0 y1 y2 y3 ... yknn]</div></blockquote></blockquote></blockquote></blockquote></blockquote><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><blockquote style="margin:0px 0px 0px 40px;border:none;padding:0px"><div>[z0 z1 z2 z3 ... zknn]</div></blockquote></blockquote></blockquote></blockquote></blockquote></blockquote><div>but this would definitely not be square. Is it a covariance matrix for all points, kind of analagous to PCA?</div><div><br></div><div>Best,</div><div><br></div><div>Joe Faraguna<div dir="ltr" class="gmail-m_-6830463424832479137gmail_signature"><div dir="ltr"></div></div></div></div>
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