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Subject: Re: Permutation of sparse matrices
Date: Wed, 14 Jan 2009 05:47:02 +0000 (UTC)
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John Montgomery <experimentmonty@gmail.com> wrote in message <25017450.1231910094719.JavaMail.jakarta@nitrogen.mathforum.org>...
> Yes, all of the matrices are meant to be symetric, as they're meant to be the representation of an undirected graph.  Basically, the permutation is just meant to be changing the order of solving a graph, such as using a natural ordering or using the ordering of the largest incidence degree first, so the rows and the columns do need to be permuted, as you gathered.
> 
> Also, the pre and post multiplication will use the same permutation matrix, as you gathered as well.  Thanks for your help with this.
> 
> John Montgomery

  As you may have gathered by now, John, given your description of how the post (on the right) multiplication matrix is defined, it results in the given permutation being performed on the matrix A columns, which accounts for the A(:,p) on the right side of the assignment.  Multiplication by the same pre multiplication matrix (on the left) will result in the inverse of this same permutation applied to the rows of A, which is the reason for the A(p,:) on the left side of the assignment.

  Are you certain this is the kind of permutation you are seeking - as contrasted with, say, the same permutation being performed on both the columns and the rows?

Roger Stafford