function x = tridlu(a,d,c,b)
% x=tridlu(a,d,c,b) computes the solution of the tridiagonal linear system
% Ax=b with lower diagonal a, main diagonal d, and upper diagonal c, using
% Gaussian elimination without pivoting.

% Check whether the input is in any way meaningful.
n = length(d);
if(length(a) ~= n-1 || length(c) ~=n-1)
    error('The dimensions of the input vectors are incompatible.');
end
if(length(b) ~= n)
    error('The dimension of b is incompatible.');
end

% Apply forward elimination to the matrix (i.e., update the main and the
% lower diagonal.
for i=1:(n-1)
    a(i) = a(i)/d(i);
    d(i+1) = d(i+1) - a(i)*c(i);
end

% Apply forward elimination to the right hand side.
for i=2:n
    b(i) = b(i) - a(i-1)*b(i-1);
end

% Back substitution.
b(n) = b(n)/d(n);
for i=n-1:-1:1
    b(i) = (b(i) - c(i)*b(i+1))/d(i);
end

x = b;