<div dir="ltr"><div class="gmail_extra"><div class="gmail_quote">On Mon, Jul 11, 2016 at 1:22 PM, Ketan Maheshwari <span dir="ltr"><<a href="mailto:ketancmaheshwari@gmail.com" target="_blank">ketancmaheshwari@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr">Matthew,<div><br></div><div>I am probably not using the right language but I meant that each element has three indices associated with it: x, y, z.</div><div><br></div><div>Here is a snapshot:</div><div><br></div><div><div>1 10 55 5.7113635929515209e-03</div><div> 1 10 56 4.2977490038287334e-03</div><div> 1 10 57 2.8719519782193204e-03</div><div> 1 10 58 1.4380140927001712e-03</div><div> 1 10 59 9.9299930690365083e-17</div><div> 1 11 0 0.0000000000000000e+00</div><div> 1 11 1 1.5658614070601917e-03</div><div> 1 11 2 3.1272842098367562e-03</div><div> 1 11 3 4.6798423857521204e-03</div></div><div><br></div><div>Where the first three columns are the coordinates and the last one is value.</div></div></blockquote><div><br></div><div>This is not a matrix. A matrix is a linear operator on some space with a finite basis: <a href="https://en.wikipedia.org/wiki/Matrix_(mathematics)">https://en.wikipedia.org/wiki/Matrix_(mathematics)</a></div><div>This is just a set of data points.</div><div><br></div><div>Most people would call this a vector, since you have an index I (which consists of each independent triple) and a value V.</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>Could you clarify the meaning of "diagonalization is not a clear concept" if it is applicable to this case.</div></div></blockquote><div><br></div><div>There is no one definition of tensor diagonalization.</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>Thank you,</div><div>--</div><div>Ketan</div><div><br></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Mon, Jul 11, 2016 at 1:15 PM, Matthew Knepley <span dir="ltr"><<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div class="gmail_extra"><div class="gmail_quote"><span>On Mon, Jul 11, 2016 at 12:05 PM, Ketan Maheshwari <span dir="ltr"><<a href="mailto:ketancmaheshwari@gmail.com" target="_blank">ketancmaheshwari@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>Hello PETSC-ers,</div><div><br></div><div>I am a research faculty at Univ of Pittsburgh trying to use PETSC/SLEPC to </div><div>obtain the diagonalization of a large matrix using Lanczos or Davidson method.</div><div><br></div><div>The matrix is a 3 dimensional dense matrix with a total of 216000 elements.</div><div><br></div><div>After looking into some of the examples in PETSC as well SLEPC implementations </div><div>it seems like most of the implementations are with 2 dimensional matrices.</div></div></blockquote><div><br></div></span><div>You will have to explain what you mean by a "3D matrix". A matrix, by definition, has only</div><div>rows and columns. You may mean a matrix generated from a 3D problem. That should pose</div><div>no extra difficulty. You may mean a 3-index tensor, in which case diagonalization is not a clear</div><div>concept.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><span><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-style:solid;border-left-color:rgb(204,204,204);padding-left:1ex"><div dir="ltr"><div>So, I was wondering if it is possible to express a 3 dimensional matrix object</div><div>compatible to PETSC so that the SLEPC API could be used to obtain </div><div>diagonalization.</div><div><br></div><div>Any suggestions or pointers to documentation or examples would be of great</div><div>help. </div><div><br></div><div>Best,</div><span><font color="#888888"><div>-- <br></div><div data-smartmail="gmail_signature"><font face="'courier new', monospace">Ketan</font><br><br></div>
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</blockquote></span></div><span><font color="#888888"><br><br clear="all"><span class=""><font color="#888888"><div><br></div>-- <br><div data-smartmail="gmail_signature">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div>
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</font></span></blockquote></div><span class=""><font color="#888888"><br><br clear="all"><div><br></div>-- <br><div data-smartmail="gmail_signature"><font face="'courier new', monospace">Ketan</font><br><br></div>
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</blockquote></div><br><br clear="all"><div><br></div>-- <br><div class="gmail_signature" data-smartmail="gmail_signature">What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener</div>
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