Given the sparsity pattern of an symmetric matrix and a symmetric permutation that reduces the proﬁle of , 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 are regarded as nonzero. If is the column index of the ﬁrst nonzero in row (), the length of row is and the proﬁle of is the sum of the lengths of the rows.
MC61 (or MC60) may be used to obtain an initial symmetric permutation.