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MC67 Refine a profile-reducing permutation of a symmetric matrix

Given the sparsity pattern of an n × n symmetric matrix A and a symmetric permutation that reduces the profile of A, this routine computes a new symmetric permutation with a smaller profile. The exchange algorithms of Hager are used to refine the given permutation.

Any zeros on the diagonal of A are regarded as nonzero. If mi is the column index of the first nonzero in row i (mi i), the length of row i is i mi + 1 and the profile of A is the sum of the lengths of the rows.

MC61 (or MC60) may be used to obtain an initial symmetric permutation.