function x=tri(n,a,d,c,b)
%TRI  Solve an  n by n  tridiagonal system.  
%>> x=tri(n,a,d,c,b)
%where
%   n = number of unknowns
%   d = diagonal elements (n length vector)
%   a = sub-diagonal (n-1 length vector)
%   c = super-diagonal (n-1 length vector)
%   b = right side of system  A x = b (n length vector)
%   x = solution (n length column vector)
%
%ELB 10/31/04; based on procedure "tri" in Cheney & Kincaid

x=zeros(n,1);            % create column vector for solution
for i=2:n
    if abs(d(i-1))<10*eps, warning('very small diagonal entry'); end
    xmult=a(i-1)/d(i-1);
    d(i)=d(i)-xmult*c(i-1);
    b(i)=b(i)-xmult*b(i-1);
end
x(n)=b(n)/d(n);
for i=n-1:-1:1
    if abs(d(i))<10*eps, warning('very small diagonal entry'); end
    x(i)=(b(i)-c(i)*x(i+1))/d(i);
end