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POParallelize Solve() for Ax=b?
 

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  1. POParallelize Solve() for Ax=b?
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    <p>Crossposted with STATS.se since this problem could straddle both STATs.se/SO <a href="https://stats.stackexchange.com/questions/17712/parallelize-solve-for-ax-b">https://stats.stackexchange.com/questions/17712/parallelize-solve-for-ax-b</a> </p> <hr> <p>I have some extremely large sparse matrices created using spMatrix function from the matrix package.</p> <p>Using the solve() function works for my Ax=b issue, but it takes a very long time. Several days. </p> <p>I noticed that <a href="http://cran.r-project.org/web/packages/RScaLAPACK/RScaLAPACK.pdf" rel="nofollow noreferrer">http://cran.r-project.org/web/packages/RScaLAPACK/RScaLAPACK.pdf</a> appears to have a function that can parallelize the solve function, however, it can take several weeks to get new packages installed on this particular server. </p> <p>The server already has the snow package installed it.</p> <p>So</p> <ol> <li>Is there a way of using snow to parallelize this operation? </li> <li>If not, are there other ways to speed up this type of operation?</li> <li>Are there other packages like RScaLAPACK? My search on RScaLAPACK seemed to suggest people had a lot of issues with it. </li> </ol> <p>Thanks.</p> <p>[EDIT] -- Additional details</p> <p>The matrices are about 370,000 x 370,000. I'm using it to solve for alpha centrality, <a href="http://en.wikipedia.org/wiki/Alpha_centrality" rel="nofollow noreferrer">http://en.wikipedia.org/wiki/Alpha_centrality</a>. I was originally using the alpha centrality function in the igraph package, but it would crash R. </p> <p>More details </p> <ul> <li>This is on a single machine with 12 cores and 96 gigs of memory (I believe)</li> <li>It's a directed graph along the lines of paper citation relationships.</li> <li>Calculating condition number and density will take awhile. Will post as it comes available.</li> <li>Will crosspost on stat.SE and will add a link back to here</li> </ul>
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    1. COCan you post info on the scale of the matrix (or matrices) involved? Depending on scale, I may have some other suggestions.
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    2. COJust saw your update. We need to go to a statistical perspective on this. Also, do you have an estimate of the lower bound of the condition number (e.g. eval1 / eval100)? Unless you're absolutely wedded to the idea of alpha centrality, it may be good to post a question about computationally expedient alternatives to the statistics StackExchange site.
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    3. CONB: If you do post a question related to this on Stats.SE, please add a link here (and a reciprocal one there) so that others may address or review one side of the coin or the other (i.e. the computational versus the statistical). Also, what kind of computing system are you attempting this on - one machine with limited RAM, one with lots of cores & lots of RAM, or a grid?
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