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function [L,U,P] = lu_rightpr (A)
%LU_RIGHTPR recursive right-looking LU, with partial pivoting.
%
% Example:
% [L,U,P] = lu_rightpr (A)
% See also: cs_demo
% Copyright 2006-2007, Timothy A. Davis.
% http://www.cise.ufl.edu/research/sparse
n = size (A,1) ;
if (n == 1)
P = 1 ;
L = 1 ;
U = A ;
else
[x,i] = max (abs (A (1:n,1))) ; % partial pivoting
P1 = eye (n) ;
P1 ([1 i],:) = P1 ([i 1], :) ;
A = P1*A ;
u11 = A (1,1) ; % (6.10)
u12 = A (1,2:n) ; % (6.11)
l21 = A (2:n,1) / u11 ; % (6.12)
[L22,U22,P2] = lu_rightpr (A (2:n,2:n) - l21*u12) ; % (6.9) or (6.13)
o = zeros(1,n-1) ;
L = [ 1 o ; P2*l21 L22 ] ; % (6.14)
U = [ u11 u12 ; o' U22 ] ;
P = [ 1 o ; o' P2] * P1 ;
end
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