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function L = cs_updown (L, c, parent, sigma) %#ok
%CS_UPDOWN rank-1 update/downdate of a sparse Cholesky factorization.
% L = cs_updown(L,c,parent) computes the rank-1 update L = chol(L*L'+c*c')',
% where parent is the elimination tree of L. c must be a sparse column
% vector, and find(c) must be a subset of find(L(:,k)) where k = min(find(c)).
% L = cs_updown(L,c,parent,'-') is the downdate L = chol(L*L'-c*c').
% L = cs_updown(L,c,parent,'+') is the update L = chol(L*L'+c*c').
% Updating/downdating is much faster than refactorizing the matrix with
% cs_chol or chol. L must not have an entries dropped due to numerical
% cancellation (use cs_chol(A,0)).
%
% Example:
% Prob = ssget ('HB/bcsstk01') ; A = Prob.A ; n = size (A,1) ;
% L = cs_chol (A,0) ;
% parent = cs_etree (A) ;
% c = sprand (L (:, floor(n/2))) ;
% L1 = cs_updown (L, c, parent) ;
% L2 = cs_chol (A + c*c', 0) ;
% norm (L1-L2, 1)
%
% See also CS_ETREE, CS_CHOL, ETREE, CHOLUPDATE, CHOL.
% CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
% SPDX-License-Identifier: LGPL-2.1+
error ('cs_updown mexFunction not found') ;
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