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function [L,U,p,q] = cs_lu (A,tol) %#ok
%CS_LU sparse LU factorization, with fill-reducing ordering.
% [L,U,p] = cs_lu(A) factorizes A(p,:) into L*U using no fill-reducing
% ordering.
%
% [L,U,p] = cs_lu(A,tol) factorizes A(p,:) into L*U using no fill-reducing
% ordering. Entries on the diagonal are given preference in partial pivoting.
%
% [L,U,p,q] = cs_lu(A) factorizes A(p,q) into L*U using a fill-reducing
% ordering q = cs_amd(A,2). Normal partial pivoting is used.
%
% [L,U,p,q] = cs_lu(A,tol) factorizes A(p,q) into L*U, using a fill-reducing
% ordering q = cs_amd(A,1). Entries on the diagonal are given preference in
% partial pivoting. With a pivot tolerance tol, the entries in L have
% magnitude 1/tol or less. tol = 1 is normal partial pivoting (with
% q = cs_amd(A)). tol = 0 ensures p = q. 0<tol<1 is relaxed partial
% pivoting; the diagonal is selected if it is >= tol * max(abs(A(:,k))).
%
% Example:
% Prob = ssget ('HB/arc130') ; A = Prob.A ; [L,U,p,q] = cs_lu (A) ;
% cspy (A (p,q)) ; cspy (L+U) ;
% norm (L*U - A(p,q), 1)
%
% See also CS_AMD, LU, UMFPACK, AMD, COLAMD.
% Copyright 2006-2012, Timothy A. Davis, http://www.suitesparse.com
error ('cs_lu mexFunction not found') ;
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