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function [p, stats] = ccolamd (S, knobs, cmember) %#ok
%CCOLAMD constrained column approximate minimum degree permutation.
% p = CCOLAMD(S) returns the column approximate minimum degree permutation
% vector for the sparse matrix S. For a non-symmetric matrix S, S(:,p)
% tends to have sparser LU factors than S. chol(S(:,p)'*S(:,p)) also tends
% to be sparser than chol(S'*S). p=ccolamd(S,1) optimizes the ordering for
% lu(S(:,p)). The ordering is followed by a column elimination tree post-
% ordering.
%
% Example:
% p = ccolamd (S)
% p = ccolamd (S,knobs,cmember)
%
% knobs is an optional one- to five-element input vector, with a default
% value of [0 10 10 1 0] if not present or empty ([ ]). Entries not present
% are set to their defaults.
%
% knobs(1): if nonzero, the ordering is optimized for lu(S(:,p)). It will
% be a poor ordering for chol(S(:,p)'*S(:,p)). This is the most
% important knob for ccolamd.
% knobs(2): if S is m-by-n, rows with more than max(16,knobs(2)*sqrt(n))
% entries are ignored.
% knobs(3): columns with more than max(16,knobs(3)*sqrt(min(m,n))) entries
% are ignored and ordered last in the output permutation (subject to the
% cmember constraints).
% knobs(4): if nonzero, aggressive absorption is performed.
% knobs(5): if nonzero, statistics and knobs are printed.
%
% cmember is an optional vector of length n. It defines the constraints on
% the column ordering. If cmember(j)=s, then column j is in constraint set
% s (s must be in the range 1 to n). In the output permutation p, all
% columns in set 1 appear first, followed by all columns in set 2, and so
% on. cmember=ones(1,n) if not present or empty. ccolamd(S,[],1:n) returns
% 1:n.
%
% p = ccolamd(S) is about the same as p = colamd(S). knobs and its default
% values differ. colamd always does aggressive absorption, and it finds an
% ordering suitable for both lu(S(:,p)) and chol(S(:,p)'*S(:,p)); it cannot
% optimize its ordering for lu(S(:,p)) to the extent that ccolamd(S,1) can.
%
% See also AMD, CSYMAMD, COLAMD, SYMAMD, SYMRCM.
% Copyright 1998-2007, Timothy A. Davis, Stefan Larimore, and Siva Rajamanickam
% Developed 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.
error ('ccolamd: mexFunction not found') ;
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