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clear
rand ('state', 0) ;
% f = 185 ;
% f = 449 ;
clf
for trials = 1:100
m = fix (100 * rand (1)) ;
n = fix (100 * rand (1)) ;
d = 0.1 * rand (1) ;
A = sprandn (m, n, d) ;
[m n] = size (A) ;
if (m < n)
A = A' ;
end
[m n] = size (A) ;
sp = sprank (A) ;
% if (sp < n)
% continue ;
% end
Aorig = A ;
% A = A (:, colamd (A)) ;
tic ;
R = qr (A) ;
t1 = toc ;
% tic ;
% [Q,R] = qr (A) ;
% t1 = toc ;
[c,h,parent] = symbfact (A, 'col') ;
rnz = sum (c) ;
tic ;
[V2,Beta2,p,R2] = cs_qr (sparse(A)) ;
t2 = toc ;
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))]
s1 = svd (full (A)) ;
s2 = svd (full (R2)) ;
if (n > 0)
err2 = norm (s1 - s2) / s1 (1)
else
err2 = 0 ;
end
fprintf ('%10.6f %10.6f cs speedup %8.3f sprank %d vs %d\n', t1, t2, t1/t2, sp, n) ;
% H2 = full (H2)
% R2 = full (R2)
subplot (2,4,1) ; spy (A) ; title ('A colamd') ;
subplot (2,4,4) ; spy (Aorig) ; title ('Aorig') ;
subplot (2,4,2) ; spy (C) ; title ('A rperm') ;
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 H') ;
drawnow
if (err2 > 1e-9)
error ('!') ;
end
if (m2 > m)
fprintf ('added %d rows, sprank %d n %d\n', m2-m, sp, n) ;
end
end
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