1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
|
function test10
%TEST10 test cs_qr
%
% Example:
% test10
% See also: testall
% Copyright 2006-2007, Timothy A. Davis.
% http://www.cise.ufl.edu/research/sparse
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') ; %#ok
rnz = sum (c) ; %#ok
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) ;
disp ('err1 = ') ;
disp (err1) ;
% [svd(A) svd(R1) svd(full(R2))]
s1 = svd (full (A)) ;
s2 = svd (full (R2)) ;
if (n > 0)
err2 = norm (s1 - s2) / s1 (1) ;
disp ('err2 = ') ;
disp (err2) ;
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
|
