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function test9
%TEST9 test cs_qr
%
% Example:
% test9
% See also: testall
% CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
% SPDX-License-Identifier: LGPL-2.1+
rand ('state', 0) ;
index = ssget ;
[ignore f] = sort (max (index.nrows, index.ncols)) ;
f = f (1:100) ;
clf
% f = 185 ;
% f = 449 ;
% f = 186
for i = f
Prob = ssget (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
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