Write a computer program to give the factorization PA LU fo

Write a computer program to give the factorization PA = LU for any given square matrix A. Use partial pivoting to switch rows. Give some examples.

clc
clear all
A=input(\'enter Adata\ \');

[m n]=size(A);

if (m == n )
L=eye(m,m);
U=A;
count1=0;
count2=0;
k=1;
x=1;
for i=1:m
if U(i,i)~=0
E=eye(m,m);
for j=i+1:m
multi=U(j,i)/U(i,i);
E(j,i)=E(j,i)-multi;
U(j,:)= U(j,:)-multi* U(i,:);
end
count1=count1+1;
ele(:,:,count1)=E;
elepos(k)=i;
k=k+1;
else
P=eye(m,m);
for y=i:m
if U(y,i)~=0
break
end
end
U([i,y],:)=U([y,i],:);
P([i,y],:)=P([y,i],:);
count2=count2+1;
per(:,:,count2)=P;
E=eye(m,m);
for j=i+1:m
multi=U(j,i)/U(i,i);
E(j,i)=E(j,i)-multi;
U(j,:)= U(j,:)-multi* U(i,:);
end
count1=count1+1;
ele(:,:,count1)=E;
perpos(x)=i;
x=x+1;
end
end
else
disp ( \'Dimension error: Matrix must be square\' );
end
P=eye(m,m);
if count2>0
for i=length(perpos):-1:1
P=P*per(:,:,i);
end
if perpos(1)>1 || count2>1
for i=1:length(elepos)
temp=eye(m,m);
for j=length(perpos):-1:i
temp=temp*per(:,:,j);
end
ele(:,:,i)=temp*ele(:,:,i)*temp\';
end
end
end
for i=1:m
for j=1:m
for k=1:m
if j>k
ele(j,k,i)=-ele(j,k,i);
end
end
end
end
for i=1:m
L=L*ele(:,:,i);
end
P
L
U