Code covered by the BSD License

# Numerical Methods Using MATLAB, 4e

### John Mathews (view profile)

23 Dec 2003 (Updated )

Companion software to accompany the book "Numerical Methods Using MATLAB"

lufact(A,B)
```function X = lufact(A,B)
%Input    - A is an N x N matrix
%	         - B is an N x 1 matrix
%Output - X is an N x 1 matrix containing the solution to AX = B.

%  NUMERICAL METHODS: Matlab Programs
% (c) 2004 by John H. Mathews and Kurtis D. Fink
%  Complementary Software to accompany the textbook:
%  NUMERICAL METHODS: Using Matlab, Fourth Edition
%  ISBN: 0-13-065248-2
%  Prentice-Hall Pub. Inc.
%  One Lake Street
%  Upper Saddle River, NJ 07458

%Initialize X, Y,the temporary storage matrix C, and the row
% permutation information matrix R

[N,N]=size(A);
X=zeros(N,1);
Y=zeros(N,1);
C=zeros(1,N);
R=1:N;

for p=1:N-1

%Find the pivot row for column p
[max1,j]=max(abs(A(p:N,p)));

%Interchange row p and j
C=A(p,:);
A(p,:)=A(j+p-1,:);
A(j+p-1,:)=C;
d=R(p);
R(p)=R(j+p-1);
R(j+p-1)=d;

if A(p,p)==0
'A is singular.  No unique solution'
break
end

%Calculate multiplier and place in subdiagonal portion of A
for k=p+1:N
mult=A(k,p)/A(p,p);
A(k,p) = mult;
A(k,p+1:N)=A(k,p+1:N)-mult*A(p,p+1:N);
end
end

%Solve for Y
Y(1) = B(R(1));
for k=2:N
Y(k)= B(R(k))-A(k,1:k-1)*Y(1:k-1);
end

%Solve for X
X(N)=Y(N)/A(N,N);
for k=N-1:-1:1
X(k)=(Y(k)-A(k,k+1:N)*X(k+1:N))/A(k,k);
end

```