function [x1,beta,v] = gen_hh(x) %GEN_HH Generate a Householder transformation. % % [x1,beta,v] = gen_hh(x) % % Given a vector x, gen_hh computes the scalar beta and the vector v % determining a Householder transformation %    H = (I - beta*v*v'), % such that H*x = +-norm(x)*e_1. x1 is the first element of H*x.  % Based on routine 'house' from Nicholas J. Higham's Test Matrix Toolbox.% Per Christian Hansen, IMM, Sept. 13, 2001. alpha = norm(x)*(sign(x(1)) + (x(1)==0)); v = x;if (alpha==0),   beta = 0; else   beta = 1/(abs(alpha)*(abs(alpha) + abs(v(1)))); end v(1) = v(1) + alpha;x1 = -alpha;