function [A] = counterexample_GEPP(n,r,u,v);
%
%	Function counterexample_GEPP generates a matrix which fails 
%	GEPP in terms of large element growth.
%       This is a generalization of the Kahan matrix.
%
% written by Ming Gu for Math221, Fall 2007. 
%
	if (nargin == 2)
		u = rand(n,r);
		v = rand(n,r);
		A = - triu(u * v');
		for k = 2:n
			umax = max(abs(A(k-1,k:n))) * (1 + 1/n);
			A(k-1,k:n)  = A(k-1,k:n) / umax;
		end
		A = A - diag(diag(A)); 
		A = A' + eye(n);
		A(1:n-1,n) = ones(n-1,1);
	else
		A = triu(u * v');
		A = A - diag(diag(A));
		A = A' + eye(n);
		A(1:n-1,n) = ones(n-1,1);
	end
	return