% 2013-02-14 18:15  UPDATE : String formating from Jenna
% 2013-02-13 17:54  UPDATE : changed how the code measures error
%                            Thanks to AARON.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Run this script to test your code problem #4
% to use backward substitution change a REF matrix
% to a RREF matrix.
%
% Warning: this is just an example testing script.
% Just because your function passes these tests DOES NOT
% ENSURE that it's flawless.  User beware.
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

num_tries = 400;  % number of matrices to test
scale = 7; % largest element size of random matrices
m = 8; % number of matrix rows
for n =7:9

disp('Running random trials');

t = 1;
while t < num_tries
	pivots=unique((0:m).*(rand(1,n)>(1.0/m)));
	pivots=pivots(2:end);
	Z = zeros(m,n);
	for i = 1:length(pivots)
		Z(i,pivots(i):end) = 1;
	end
	A = floor(rand(m,n)*scale-(scale-1)/2).*Z;
	for i = 1:length(pivots)
		if 0 == A(i,pivots(i))
			A(i,pivots(i)) = (floor(rand(1)*scale)+1)*((rand(1)>0.5)*2.-1);
			if i < m
				A(i+1:end,(pivots(i)+1)) = 0;
			end
		end
	end
	if rank(A) ~= length(pivots)
		continue
	end

	RREF_exact = rref(A);
	RREF = transform_ref_to_rref(A);
	er = max(max(abs(RREF - RREF_exact)));
	assert( abs(er) < 1e-10 );
	t = t + 1;
end
disp('All trials passed!');