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function [L,U,y,x]=LU(A,B)
7 I3 l& Z+ |5 X9 E' G/ an=length(A);
: d0 ]& }! o# r' eL=eye(n);& r( p7 b+ Q" L
U=zeros(n,n);
U1 m! x6 z5 ]8 }' G9 D! ^! g( R ]for k=1:n
5 i" D* e4 y! c! y0 Y+ o for j=k:n
. g% Y% K! g6 M, U/ `9 d c=0;! v' \1 R0 w" r- \9 a$ f
for i=1:k-14 P- |3 q/ Q. k
c=c+L(k,i)*U(i,j);/ r% v6 {8 v, g; o% m4 r1 t; O: n$ x
end
# e; r, ^3 k1 W) T9 a U(k,j)=A(k,j)-c;, R& u" C+ C0 s W
end
. e5 B4 l! V/ o% f, U if U(k,k)==05 ~. e7 g4 v" y, e- d4 Z
for i=k+1:n
6 e4 V9 X0 a) j& ] z=i;
, l. J' B6 f/ ] p! e if U(k,i)~=00 Z. a; @0 @9 x4 g Z
break;end
' d5 d0 b9 s: O: w2 t L B end, [, w r: W0 ?) Z& H
for i=1:k
5 C+ H2 l& t3 a" E a=U(i,k);U(i,k)=U(i,z);U(i,z)=a;
9 I, @7 @4 Y( |. k/ A/ W' H end
" p1 a* b3 J P for i=1:n
7 ?5 A$ |( @% O7 l a=A(i,k);A(i,k)=A(i,z);A(i,z)=a;4 ]" j/ ~" {4 |( l* b& q t
end8 W# Y5 [6 Z9 \+ K7 u* d
end
: Y; a4 }& O! m) h1 K for i=k+1:n5 ]' y# G, p4 M9 }
c=0;
5 \8 L9 n; W, ^( \ for q=1:k-1
. Y# ~& @6 g8 t1 I/ r' ] c=c+L(i,q)*U(q,k);
& u9 F1 A: |5 C* O+ N end
7 G, g! U7 @: ?6 s# _ h" p6 f L(i,k)=(A(i,k)-c)/U(k,k);& }1 i. b' \1 m
end# `& M% P, G. s+ Q9 u4 ^; A
end
$ x. F! b" K b4 i: P for k=1:n! U6 ]( T+ ^8 \) i/ n
c=0;
: X; B( m% j% U for i=1:k-1
7 X+ o! D; q8 r5 f) {9 R2 \3 k c=c+L(k,i)*y(i);
6 s( O5 K1 [$ z& r# \ end" T& u8 N0 x8 w2 C- A3 z
y(k)=(B(k)-c)/L(k,k);; c' D0 Z/ m1 S& @! `8 x* |( P
end
7 l' u4 G: G. f( R4 @ for k=n:-1:1. v4 ^8 g$ E0 f
c=0;& M, C% ^; E$ K2 D3 R, A4 @! S1 g
for i=k+1:n7 G5 S# A* Y- r8 H2 H5 D
c=c+U(k,i)*x(i);
1 j% J% U x. O0 J end' b$ K; J9 b$ C/ q6 Q- W
x(k)=(y(k)-c)/U(k,k);4 Y( o6 k0 \( S9 y: U* W. J0 ]1 @
end
: k( u5 X3 f6 Q- B& @
' N7 T2 V! p0 |4 W4 y2 D |