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
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
|
function sparseinv_test (extensive)
%SPARSEINV_TEST tests the sparseinv function.
%
% Example
% sparseinv_test ; % basic test
% sparseinv_test (1) ; % extensive test (requires ssget)
%
% See also sparseinv, sparseinv_install, ssget.
% Copyright 2011, Timothy A. Davis, http://www.suitesparse.com
if (nargin < 1)
extensive = 0 ;
end
load west0479 ;
A = west0479 ;
for k = 1:2
[Z, Zpattern, L, D, U, P, Q, stats] = sparseinv (A) ;
n = size (A,1) ;
I = speye (n) ;
S = inv (A) ;
Snorm = norm (S, 1) ;
e1 = norm (Zpattern.*(Z-S), 1) / Snorm ;
e2 = norm ((L+I)*D*(U+I) - P*A*Q, 1) / norm (A,1) ;
c = condest (A) ;
fprintf ('west0479: errors %g %g condest %g : ', e1, e2, c) ;
if (e1 > 1e-10 || e2 > 1e-10)
error ('west0479 test failed') ;
end
fprintf ('ok\n') ;
disp (stats) ;
% create a symmetric positive definite matrix to test with
if (k == 1)
A = A+A' + 1e6*I ;
end
end
% check error-handling
fprintf ('testing error handling (errors below are expected)\n') ;
ok = 1 ;
A = ones (2) ;
try
Z1 = sparseinv (A) ; %#ok
ok = 0 ;
catch me
fprintf (' expected error: %s\n', me.message) ;
end
A = sparse (ones (3,2)) ;
try
Z2 = sparseinv (A) ; %#ok
ok = 0 ;
catch me
fprintf (' expected error: %s\n', me.message) ;
end
A = sparse (ones (3)) ;
try
Z3 = sparseinv (A) ; %#ok
ok = 0 ;
catch me
fprintf (' expected error: %s\n', me.message) ;
end
A = 1i * sparse (ones (3)) ;
try
Z4 = sparseinv (A) ; %#ok
ok = 0 ;
catch me
fprintf (' expected error: %s\n', me.message) ;
end
if (~ok)
error ('error-handling tests failed') ;
end
% now try with lots of matrices from the SuiteSparse Matrix Collection
if (extensive && exist ('ssget', 'file') == 2)
fprintf ('Now doing extensive tests with SuiteSparse Matrix Collection:\n') ;
dofigures = (exist ('cspy', 'file') == 2) ;
if (dofigures)
clf ;
end
index = ssget ;
f = find ((index.nrows == index.ncols) & (index.isReal == 1)) ;
[ignore,i] = sort (index.nrows (f)) ; %#ok
f = f (i) ;
nmat = length (f) ;
s = warning ('off', 'MATLAB:nearlySingularMatrix') ;
for k = 1:nmat
id = f (k) ;
Prob = ssget (id, index) ;
A = Prob.A ;
n = size (A,1) ;
I = speye (n) ;
fprintf ('id: %4d n: %4d : %-30s', id, n, Prob.name) ;
Z = [ ] ;
try
[Z, Zpattern, L, D, U, P, Q] = sparseinv (A) ;
catch me
fprintf ('%s', me.message) ;
end
if (~isempty (Z))
e = norm ((L+I) * D * (U+I) - P*A*Q, 1) / norm (A,1) ;
fprintf ('errs: %12.3e ', e) ;
if (e > 1e-10)
error ('error in factorization too high') ;
end
S = inv (A) ; % normally S has MANY nonzero entries
Snorm = norm (S,1) ;
E = abs (Zpattern .* (Z-S)) / Snorm ;
e = norm (E, 1) ;
c = condest (A) ;
fprintf (' %12.3e condest: %12.2e', e, c) ;
if (e/c > 1e-8)
error ('error in sparseinv too high') ;
end
fprintf (' ok') ;
if (dofigures)
subplot (2,2,1) ; cspy (A) ;
title (Prob.name, 'Interpreter', 'none') ;
subplot (2,2,2) ; cspy (P*A*Q) ; title ('P*A*Q') ;
subplot (2,2,3) ; cspy (Z) ; title ('sparse inverse') ;
subplot (2,2,4) ; cspy (S) ; title ('inverse') ;
drawnow
end
end
fprintf ('\n') ;
if (n >= 300)
break ;
end
end
warning (s) ; % restore warning status
end
fprintf ('All sparseinv tests passed.\n') ;
|
