% Tridiagonal linear systems subroutine

function [x]=Tridiag(A,B,N)

% Matrices L and U corresponding to the decomposition A=LU
l=zeros(N);
u=zeros(N);
u(1,1)=1;
l(1,1)=A(1,1);
u(1,2)=A(1,2)/l(1,1);
for i=2:N-1
   l(i,i-1)=A(i,i-1);
   l(i,i)=A(i,i)-l(i,i-1)*u(i-1,i);
   u(i,i+1)=A(i,i+1)/l(i,i);
   u(i,i)=1;
end
l(N,N-1)=A(N,N-1);
l(N,N)=A(N,N)-l(N,N-1)*u(N-1,N);
u(N,N)=1;
disp('LU Decomposition');
disp(l);
disp(u);

% Solving the linear system

z(1)=B(1)/l(1,1);
for i=2:N
      z(i)= (B(i)-l(i,i-1)*z(i-1))/l(i,i);
end
%disp(z);
x(N)=z(N);
for j=1:N-1
   x(N-j)=z(N-j)-x(N-j+1)*u(N-j,N-j+1);
 end