On Tue, Jan 4, 2011 at 12:30 AM, Gaurish Telang <span dir="ltr"><<a href="mailto:gaurish108@gmail.com">gaurish108@gmail.com</a>></span> wrote:<br><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
<span style="font-family:arial, sans-serif;font-size:13px;border-collapse:collapse">I have 2 semi sparse matrices (see sparsity plots) attached and I wanted to get to know some basic information about them. </span></blockquote>
<div><br></div><div>There are no attachments.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><span style="font-family:arial, sans-serif;font-size:13px;border-collapse:collapse"><div>
1. How does one calculate the rank of a matrix in PETSc. Is the answer returned approximate or exact for matrices of dimension say 2500X1200</div></span></blockquote><div><br></div><div>You need a rank revealing factorization. I know of no sparse packages for this.</div>
<div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><span style="font-family:arial, sans-serif;font-size:13px;border-collapse:collapse"><div>2. How good are the sparse sovlers for Ax=b that PETSc employs when A is a dense full rank square matrix of size 2000x2000.</div>
</span></blockquote><div><br></div><div>I think you mean, "how well do Krylov solvers work for dense matrices?". Solver performance depends</div><div>heavily on the characteristics of the matrix. There are no general statements that can be made about</div>
<div>Krylov solvers.</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;"><span style="font-family:arial, sans-serif;font-size:13px;border-collapse:collapse"><div>
3. In my case the matrices are mostly sparse but they tend to get dense towards the bottom. What matrix format is most efficent for handling such matrices? </div></span></blockquote><div><br></div><div>You might be able to handle this with a sparse matrix A + an outer product of vectors. However, it</div>
<div>depends on your problem.</div><div><br></div><div> Matt </div></div>-- <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<br>