## modelled after xLARFG

function [x, tau, alpha] = make_house(x)
  ## usage: [h, tau, alpha] = make_house(x)
  ##
  ## Returns the Householder reflection that eliminates input vector x.
  ## So x - tau*h*h'*x == [alpha; 0; 0; ...].
  ## 

  if nargin != 1,
    usage ("make_house (vector)");
  endif
  if !isvector(x),
    error ("make_house: expecting vector argument.");
  endif

  sg = -sign(x(1));
  if (sg == 0), sg = 1; endif
  alpha = sg * norm(x,2);

  safmin = realmin(1.0)/eps;
  cnt = 0;
  if abs(alpha) < safmin,
    while abs(alpha) < safmin,
      x /= safmin;
      alpha /= safmin;
      ++cnt;
    endwhile
    alpha = sg * norm(x, 2);
  endif

  tau = (alpha - x(1)) / alpha;
  x(2:size(x,1)) /= (x(1) - alpha);
  x(1) = 1;

  if cnt > 0,
    for j=1:cnt, alpha *= safmin; endfor
  endif

endfunction