Could you please help me to write a MATLAB code? Thanks!

function [L,U,p]=lu_fac_pp(A)

n=size(A,1)

p=zeros(n,1)

for k=1:n

p(k)=k;

end

for k=1:n-1

......... (I need to choose max pivot entry in abs value in this loop)

.........(I need to check whether A is not invertible in this loop)

and return

if r not=k, then swap entire r~k with entire row r

...... (I need to do Gauss elimination in this part (store the multiplying vectors))

end

................check abs(A(n,n)) to find whether A is not invertible

L=tril(A,-1)+eye(n);

U=tril(A);

%%%%%%%%%%%%%

Command Window:

>> A=[1,1,0,3 ; 2,1,-1,1 ; 3,-1,-1,2 ; -1,2,6,-1]

>>b=[4;1;-3;4]

>>[L,U,p] = lu_fac_pp(A)

L=[ 1,0,0,0; -1/3,1,0,0; 2/3,1,1,0;1/3,4/5,3/10,1]

U=[3,-1,-1,2; 0,5/6,17/3,-1/3; 0,0,-6,0; 0,0,0,13/5]

p=[3;4;2;1]

>> c=perm_b(b,p)

c=[-3;4;1;4]

>>d=ult_sys(L,c)

d=[-3;3;0;2.6]

>> x= ut_sys(U,d)

x=[-1;2;0;1]