function test9
%TEST9 test cs_qr
%
% Example:
%   test9
% See also: testall

%   Copyright 2006-2007, Timothy A. Davis.
%   http://www.cise.ufl.edu/research/sparse

rand ('state', 0) ;

index = UFget ;
[ignore f] = sort (max (index.nrows, index.ncols)) ;
f = f (1:100) ;
clf

% f = 185 ;
% f = 449 ;
% f = 186

for i = f
    Prob = UFget (i) ;
    disp (Prob) ;
    A = Prob.A ;
    [m n] = size (A) ;
    if (m < n)
	A = A' ;
    end
    [m n] = size (A) ;
    sp = sprank (A) ;
%    if (sprank (A) < min (m,n))
%	continue
%    end


    for cmplex = 0:double(~ispc)

	if (cmplex)
	    A = A + 1i * sprand (A) ;
	end

	Aorig = A ;

	A = A (:, colamd (A)) ;
	s1 = svd (full (A)) ;

	if (cmplex)
	    try
		tic ;
		R = chol (A'*A) ;
		t1 = toc ;						    %#ok
	    catch
		fprintf ('chol (A''*A) failed\n') ;
		R = [ ] ;
	    end
	else
	    tic ;
	    R = qr (A) ;
	    t1 = toc ;							    %#ok
	end

	% tic ;
	% [Q,R] = qr (A) ;
	% t1 = toc ;

	[c,h,parent] = symbfact (A, 'col') ;
	rnz = sum (c) ;							    %#ok
	tic ;
	[V2,Beta2,p,R2] = cs_qr (sparse(A)) ;
	t2 = toc ;							    %#ok

	v2 = full (V2) ;
	if (any (spones (v2) ~= spones (V2)))
	    error ('got zeros!') ;
	end

	C = A ;
	m2 = size (V2,1) ;
	if (m2 > m)
	    C = [A ; sparse(m2-m, n)] ;
	end
	C = C (p,:) ;

    %    [H1,R1] = myqr (C) ;
    %    err1 = norm (R1-R2,1) / norm (R1)
    %    % [svd(A) svd(R1) svd(full(R2))]
    %    s2 = svd (full (R2)) ;
    %    err2 = norm (s1 - s2) / s1 (1) 
    %    fprintf ('%10.6f %10.6f  cs speedup %8.3f sprank %d n %d\n', ...
    %	t1, t2, t1/t2, sp, n) ;
    %    err2

	% left-looking:
	[V,Beta3,R3] = qr_left (C) ;					    %#ok
	s3 = svd (full (R2)) ;
	err3 = norm (s1 - s3) / s1 (1) ;
	disp ('err3 = ') ; disp (err3) ;
	if (err3 > 1e-12)
	    error ('!') ;
	end

	% right-looking:
	[V,Beta4,R4] = qr_right (C) ;					    %#ok
	s4 = svd (full (R2)) ;
	err4 = norm (s1 - s4) / s1 (1) ;
	disp ('err4 = ') ; disp (err4) ;
	if (err4 > 1e-12)
	    error ('!') ;
	end

	% H2 = full (H2)
	% R2 = full (R2)

	subplot (2,4,1) ; spy (A) ;		title ('A colamd') ;
	subplot (2,4,2) ; spy (C) ;		title ('A rperm') ;
	subplot (2,4,3) ; treeplot (parent) ;
	subplot (2,4,4) ; spy (Aorig) ;	title ('Aorig') ;
	subplot (2,4,5) ; spy (abs(R2)>0) ;	title ('spqr R, no zeros') ;
	subplot (2,4,6) ; spy (R) ;		title ('matlab R') ;
	subplot (2,4,7) ; spy (R2) ;	title ('spqr R') ;
	subplot (2,4,8) ; spy (V2) ;	title ('spqr V') ;
	drawnow

    %    if (err2 > 1e-9)
    %	error ('!') ;
    %    end
	if (m2 > m)
	    fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ;
	end
	% pause
    end

end
