function [B,gamma] = counterexample_hager(n)
%
% This function generates nxn matrices
% on which Hager's condition estimator
% can utterly fail.
%
% Written by Ming Gu for Math 221, Fall 2007
%
% Warning: This code only works properly for
% n > 2.
%
%
% hager's condition number estimator will not 
% be able to detect the magnitude of B(2:n,2:n).
% Hence one can make the estimator look very bad
% by choosing very large values of scl.
%
  e   = ones(n-1,1); e = e/norm(e);
  E   = eye(n-1) - e*e';
  Bhat= E*randn(n-1,n-1)*E;
  scl = 1e10;
  b   = rand(n-1,1);
  B   = [rand,b';b,scl*Bhat];
  kl  = 10;
  gamma = hager(B,kl);
  return