File: lu_left.m

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ufsparse 1.2-7
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function [L,U,P] = lu_left (A)
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