function [p, varargout] = symamd (S, varargin)

%SYMAMD Symmetric approximate minimum degree permutation.

%    P = SYMAMD(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 SYMAMD 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 much faster and generates comparable orderings.

%    The ordering is followed by an elimination tree post-ordering.

%

%    Usage:  P = symamd (S)

%            [P, stats] = symamd (S, knobs)

%

%    knobs is an optional one- to two-element input vector.  If S is n-by-n,

%    then rows and columns with more than max(16,knobs(1)*sqrt(n)) entries are

%    removed prior to ordering, and ordered last in the output permutation P.

%    No rows/columns are removed if knobs(1)<0.  If knobs(2) is nonzero, stats

%    and knobs are printed.  The default is knobs = [10 0].  Note that knobs

%    differs from earlier versions of symamd.

%

%    Type the command "type symamd" for a description of the optional stats

%    output and for the copyright information.

%

%    Authors: S. Larimore and T. Davis, University of Florida.  Developed in

%       collaboration with J. Gilbert and E. Ng.  Version 2.5.

%

%    Acknowledgements: This work was supported by the National Science

%       Foundation, under grants DMS-9504974 and DMS-9803599.

%

%    See also AMD, COLAMD, COLPERM, SYMRCM.

%  Used by permission of the Copyright holder.  This version has been modified

%  by The MathWorks, Inc. and their revision information is below:

%

%  Additional Notice from the original authors is below:

%    Notice:

%

%	Copyright (c) 1998-2006, Timothy A. Davis, All Rights Reserved.

%

%    Availability:

%

%       colamd and symamd are available at

%       http://www.cise.ufl.edu/research/sparse

%-------------------------------------------------------------------------------

% perform the symamd ordering:

%-------------------------------------------------------------------------------

[p, varargout{1:nargout-1}] = symamdmex(S, varargin{:}); 

%-------------------------------------------------------------------------------

% symmetric elimination tree post-ordering:

%-------------------------------------------------------------------------------

[~, q] = etree(S(p,p)); 

p = p(q);