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function [L,U,P] = lu_left (A)
%LU_LEFT left-looking LU factorization.
% Example:
% [L,U,P] = lu_left (A)
% See also: cs_demo
% CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
% SPDX-License-Identifier: LGPL-2.1+
n = size (A,1) ;
P = eye (n) ;
L = zeros (n) ;
U = zeros (n) ;
for k = 1:n
x = [ L(:,1:k-1) [ zeros(k-1,n-k+1) ; eye(n-k+1) ]] \ (P * A (:,k)) ;
U (1:k-1,k) = x (1:k-1) ; % the column of U
[a i] = max (abs (x (k:n))) ; % find the pivot row i
i = i + k - 1 ;
L ([i k],:) = L ([k i], :) ; % swap rows i and k of L, P, and x
P ([i k],:) = P ([k i], :) ;
x ([i k]) = x ([k i]) ;
U (k,k) = x (k) ;
L (k,k) = 1 ;
L (k+1:n,k) = x (k+1:n) / x (k) ; % divide the pivot column by U(k,k)
end
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