function [p, stats] = csymamd (S, knobs, cmember) %#ok %CSYMAMD constrained symmetric approximate minimum degree permutation % P = CSYMAMD(S) for a symmetric positive definite matrix S, returns the % permutation vector p such that S(p,p) tends to have a sparser Cholesky % factor than S. Sometimes CSYMAMD works well for symmetric indefinite % matrices too. The matrix S is assumed to be symmetric; only the % strictly lower triangular part is referenced. S must be square. Note % that p=amd(S) is faster, but does not allow for a constrained ordering. % The ordering is followed by an elimination tree post-ordering. % % See also AMD, CCOLAMD, COLAMD, SYMAMD. % % Example: % p = csymamd(S) % [p stats] = csymamd(S,knobs,cmember) % % knobs is an optional one- to three-element input vector, with a default % value of [10 1 0] if present or empty ([ ]). Entries not present are set % to their defaults. % % knobs(1): If S is n-by-n, then rows and columns with more than % max(16,knobs(1)*sqrt(n)) entries are ignored, and ordered last in the % output permutation (subject to the cmember constraints). % knobs(2): if nonzero, aggressive absorption is performed. % knobs(3): if nonzero, statistics and knobs are printed. % % Type the command "type csymamd" for a description of the optional stats % output. % % cmember is an optional vector of length n. It defines the constraints on % the ordering. If cmember(j)=s, then row/column j is in constraint set s % (s must be in the range 1 to n). In the output permutation p, % rows/columns in set 1 appear first, followed by all rows/columns in set 2, % and so on. cmember=ones(1,n) if not present or empty. csymamd(S,[],1:n) % returns 1:n. % % p = csymamd(S) is about the same as p = symamd(S). knobs and its default % values differ. % % Authors: S. Larimore, T. Davis (Univ of Florida), and S. Rajamanickam, in % collaboration with J. Gilbert and E. Ng. Supported by the National % Science Foundation (DMS-9504974, DMS-9803599, CCR-0203270), and a grant % from Sandia National Lab. See http://www.cise.ufl.edu/research/sparse % for ccolamd, csymamd, amd, colamd, symamd, and other related orderings. % % See also AMD, CCOLAMD, COLAMD, SYMAMD, SYMRCM. % ---------------------------------------------------------------------------- % CCOLAMD version 2.5. % Copyright 2005, Univ. of Florida. Authors: Timothy A. Davis, % Sivasankaran Rajamanickam, and Stefan Larimore % See License.txt for the Version 2.1 of the GNU Lesser General Public License % http://www.cise.ufl.edu/research/sparse % ---------------------------------------------------------------------------- % stats(1): number of dense or empty rows removed prior to ordering % stats(2): number of dense or empty columns removed prior to ordering. % These rows and columns are placed last in their constraint set. % stats(3): number of garbage collections performed. % stats (4:7) provide information if COLAMD was able to continue. The % matrix is OK if stats (4) is zero, or 1 if invalid. stats (5) is the % rightmost column index that is unsorted or contains duplicate entries, % or zero if no such column exists. stats (6) is the last seen duplicate % or out-of-order row index in the column index given by stats (5), or zero % if no such row index exists. stats (7) is the number of duplicate or % out-of-order row indices. % % stats (8:20) is always zero in the current version of COLAMD (reserved % for future use). error ('csymamd: mexFunction not found') ;