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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'>> It can be further optimized using the Woodbury identity for two cases –<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'>> rank <= size or rank >= size to reduce the size of auxiliary internal Cholesky solve.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'>Sorry, that’s wrong. I meant rank <= size/2 or rank >= size/2. Size here<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'>refers to square matrix size, but this analysis can be done for rectangular<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'>case too.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'>Chetan<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'><o:p> </o:p></span></p><div style='border:none;border-left:solid blue 1.5pt;padding:0in 0in 0in 4.0pt'><div><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> Chetan Jhurani [mailto:chetan.jhurani@gmail.com] <br><b>Sent:</b> Monday, December 19, 2011 11:35 AM<br><b>To:</b> 'PETSc users list'<br><b>Subject:</b> RE: [petsc-users] Pseudoinverse of a large matrix<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'>Couple of optimizations not there currently.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'><o:p> </o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'><span style='mso-list:Ignore'>1.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'>It can be changed to use sparse RRQR factorization for sparse input matrix.<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo2'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'><span style='mso-list:Ignore'>2.<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'>It can be further optimized using the Woodbury identity for two cases –<o:p></o:p></span></p><p class=MsoListParagraph><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'>rank <= size or rank >= size to reduce the size of auxiliary internal Cholesky solve.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'>Chetan<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Verdana","sans-serif"'><o:p> </o:p></span></p><div style='border:none;border-left:solid blue 1.5pt;padding:0in 0in 0in 4.0pt'><div><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> <a href="mailto:petsc-users-bounces@mcs.anl.gov">petsc-users-bounces@mcs.anl.gov</a> [<a href="mailto:petsc-users-bounces@mcs.anl.gov">mailto:petsc-users-bounces@mcs.anl.gov</a>] <b>On Behalf Of </b>Modhurita Mitra<br><b>Sent:</b> Monday, December 19, 2011 11:01 AM<br><b>To:</b> PETSc users list<br><b>Subject:</b> Re: [petsc-users] Pseudoinverse of a large matrix<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal style='margin-bottom:12.0pt'>I am trying to express the radiation pattern of an antenna in terms of spherical harmonic basis functions. I have radiation pattern data at N=324360 points. Therefore, my matrix is spherical harmonic basis functions evaluated till order sqrt(N) (which makes up at total of N elements), evaluated at N data points. So this is a linear least squares problem, and I have been trying to solve it by finding its pseudoinverse which uses SVD. The elements of the matrix are complex, and the matrix is non-sparse. I have solved it in MATLAB using a subsample of the data, but MATLAB runs out of memory while calculating the SVD at input matrix size 2500 X 2500. I need to solve this problem using the entire data.<br><br>I was thinking of using SLEPc because I found a ready-to-use code which computes the SVD of a complex-valued matrix ( <a href="http://www.grycap.upv.es/slepc/documentation/current/src/svd/examples/tutorials/ex14.c.html">http://www.grycap.upv.es/slepc/documentation/current/src/svd/examples/tutorials/ex14.c.html</a> ). I don't know how to use either PETSc or SLEPc (or Elemental) yet, so I am trying to figure out where to start and what I should learn. <br><br>Thanks,<br>Modhurita<o:p></o:p></p><div><p class=MsoNormal>On Mon, Dec 19, 2011 at 12:31 PM, Matthew Knepley <<a href="mailto:knepley@gmail.com">knepley@gmail.com</a>> wrote:<o:p></o:p></p><div><p class=MsoNormal>On Mon, Dec 19, 2011 at 12:21 PM, Modhurita Mitra <<a href="mailto:modhurita@gmail.com" target="_blank">modhurita@gmail.com</a>> wrote:<o:p></o:p></p></div><div><div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'><p class=MsoNormal>Hi,<br><br>I have to compute the pseudoinverse of a 324360 X 324360 matrix. Can PETSc compute the SVD of this matrix without parallelization? If parallelization is needed, do I need to use SLEPc?<o:p></o:p></p></blockquote><div><p class=MsoNormal><o:p> </o:p></p></div></div><div><p class=MsoNormal>With enough memory, yes. However, I am not sure you want to wait. I am not sure how SLEPc would help here.<o:p></o:p></p></div><div><p class=MsoNormal>From the very very little detail you have given, you would need parallel linear algebra, like Elemental. However,<o:p></o:p></p></div><div><p class=MsoNormal>I would start out from a more fundamental viewpoint. Such as replacing "compute the psuedoinverse" with<o:p></o:p></p></div><div><p class=MsoNormal>"solve a least-squares problem" if that is indeed the case.<o:p></o:p></p></div><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal> Matt<o:p></o:p></p></div><div><p class=MsoNormal> <o:p></o:p></p></div><blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;margin-left:4.8pt;margin-top:5.0pt;margin-right:0in;margin-bottom:5.0pt'><p class=MsoNormal><br>Thanks,<br>Modhurita<o:p></o:p></p></blockquote></div><p class=MsoNormal><span style='color:#888888'><br><br clear=all><o:p></o:p></span></p><div><p class=MsoNormal><span style='color:#888888'><o:p> </o:p></span></p></div><p class=MsoNormal><span style='color:#888888'>-- <br>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</span><o:p></o:p></p></div><p class=MsoNormal><o:p> </o:p></p></div></div></div></body></html>