You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: lu_left.m
    path of file: ./repos/SuiteSparse/CXSparse/MATLAB/Test
    
    the code of the file until where you have to start completion: 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.

    
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