function T = tridag(A)
% usage: T = tridag(A)
% description: given mxm A that is real symmetric, reduces
% it to tridiagonal form T and returns T. 

m = size(A,1);
T = A;
for k = 1:m-2
  x = T(k+1:m,k);
  x(1) = ((x(1)>=0)-(x(1)<0))*norm(x) + x(1);
  x = x/norm(x);
  T(k+1:m,k:m) = T(k+1:m,k:m) - 2*x*(x'*T(k+1:m,k:m));
  T(1:m,k+1:m) = T(1:m,k+1:m) - 2*(T(1:m,k+1:m)*x)*x';
end
T = triu(T) + triu(T,1)';