/* -*- MaTX -*-
 *
 *  NAME
 *      rsf2csf() - Real Schur to complex Schur form conversion
 *
 *  SYNOPSIS
 *      {Uo,To} = rsf2csf(Ui,Ti)
 *           Matrix Uo,To;
 *           Matrix Ui,Ti;
 *
 *  DESCRIPTION
 *      rsf2csf() converts a real upper quasi-triangular Schur form 
 *      to a complex upper triangular Schur form.
 *
 *  SEE ALSO
 *      schur
 */

Func List rsf2csf(Ui, Ti)
	Matrix Ui, Ti;
{
	Integer i,n;
	Real r, s;
	Complex c;
	CoMatrix To, Uo, Q, mu;

	n = length(Ti);

	To = (Ti,:);
	Uo = (Ui,:);

	for (i = n; i > 1; i--) {
		s = abs(To(i-1,i-1)) + abs(To(i,i));

		if (abs(To(i,i-1)) > EPS) {
			mu = eigval(To(i-1:i,i-1:i)) .- To(i,i);
			r = frobnorm([mu(1), To(i,i-1)]);

			if (r >= EPS) {
				c = mu(1)/r;
				s = Re(To(i,i-1))/r;
			} else {
				c = mu(1);
				s = Re(To(i,i-1));
			}

			Q = [[c#, s][-s, c]];
			To(i-1:i,i-1:n) = Q * To(i-1:i,i-1:n);
			To(1:i,i-1:i)   = To(1:i,i-1:i) * Q#;
  			Uo(1:n,i-1:i)   = Uo(1:n,i-1:i) * Q#;
		}
		To(i,i-1) = 0.0;
	}
	return {Uo, To};
}