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t_mplinsolve.m
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t_mplinsolve.m
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function t_mplinsolve(quiet)
% t_mplinsolve - Tests of mplinsolve, MIPS/|MATPOWER| linear solvers.
% ::
%
% t_mplinsolve
% t_mplinsolve(quiet)
% MIPS
% Copyright (c) 2015-2024, Power Systems Engineering Research Center (PSERC)
% by Ray Zimmerman, PSERC Cornell
%
% This file is part of MIPS.
% Covered by the 3-clause BSD License (see LICENSE file for details).
% See https://github.com/MATPOWER/mips for more info.
if nargin < 1
quiet = 0;
end
t_begin(180, quiet);
isoctave = exist('OCTAVE_VERSION', 'builtin') == 5;
if isoctave
lu_warning_id = 'Octave:lu:sparse_input';
s = warning('query', lu_warning_id);
warning('off', lu_warning_id);
end
%% non-sparse A matrix crashes some MATLAB lu() calls on certain
%% combinations of MATLAB and macOS versions
mlv = have_feature('matlab', 'vnum');
skipcrash = ~isempty(mlv) && mlv < 8.003 && mlv > 7.013 && ...
strcmp(computer, 'MACI64');
ijs = [
1 1 1205.63;
4 1 -1205.63;
25 1 17.3611;
28 1 -17.3611;
43 1 1;
2 2 1024;
8 2 -1024;
26 2 16;
32 2 -16;
3 3 1164.84;
6 3 -1164.84;
27 3 17.0648;
30 3 -17.0648;
1 4 -1205.63;
4 4 2201.34;
5 4 -453.695;
9 4 -542.009;
13 4 0.776236;
14 4 -0.451721;
18 4 -0.324515;
25 4 -17.3611;
28 4 39.4759;
29 4 -10.5107;
33 4 -11.6041;
37 4 -3.30738;
38 4 1.94219;
42 4 1.36519;
4 5 -453.695;
5 5 581.372;
6 5 -127.677;
13 5 -0.451721;
14 5 0.568201;
15 5 -0.11648;
28 5 -10.5107;
29 5 16.0989;
30 5 -5.58824;
37 5 1.94219;
38 5 -3.2242;
39 5 1.28201;
3 6 -1164.84;
5 6 -127.677;
6 6 1676.74;
7 6 -384.227;
14 6 -0.11648;
15 6 0.163059;
16 6 -0.0465791;
27 6 -17.0648;
29 6 -5.58824;
30 6 32.4374;
31 6 -9.78427;
38 6 1.28201;
39 6 -2.4371;
40 6 1.15509;
6 7 -384.227;
7 7 1141.16;
8 7 -756.935;
15 7 -0.0465791;
16 7 0.371828;
17 7 -0.325249;
30 7 -9.78427;
31 7 23.4822;
32 7 -13.698;
39 7 1.15509;
40 7 -2.77221;
41 7 1.61712;
2 8 -1024;
7 8 -756.935;
8 8 1925.77;
9 8 -144.836;
16 8 -0.325249;
17 8 0.844105;
18 8 -0.518855;
26 8 -16;
31 8 -13.698;
32 8 35.6731;
33 8 -5.97513;
40 8 1.61712;
41 8 -2.80473;
42 8 1.1876;
4 9 -542.009;
8 9 -144.836;
9 9 686.845;
13 9 -0.324515;
17 9 -0.518855;
18 9 0.84337;
28 9 -11.6041;
32 9 -5.97513;
33 9 17.5792;
37 9 1.36519;
41 9 1.1876;
42 9 -2.55279;
10 10 1207.63;
13 10 -1205.63;
34 10 17.3611;
37 10 -17.3611;
11 11 1026;
17 11 -1024;
35 11 16;
41 11 -16;
12 12 1166.84;
15 12 -1164.84;
36 12 17.0648;
39 12 -17.0648;
4 13 0.776236;
5 13 -0.451721;
9 13 -0.324515;
10 13 -1205.63;
13 13 2190.83;
14 13 -447.892;
18 13 -535.137;
28 13 3.30738;
29 13 -1.94219;
33 13 -1.36519;
34 13 -17.3611;
37 13 39.1419;
38 13 -10.5107;
42 13 -11.6041;
4 14 -0.451721;
5 14 0.568201;
6 14 -0.11648;
13 14 -447.892;
14 14 573.221;
15 14 -122.862;
28 14 -1.94219;
29 14 3.2242;
30 14 -1.28201;
37 14 -10.5107;
38 14 15.5829;
39 14 -5.58824;
5 15 -0.11648;
6 15 0.163059;
7 15 -0.0465791;
12 15 -1164.84;
14 15 -122.862;
15 15 1669.87;
16 15 -379.651;
29 15 -1.28201;
30 15 2.4371;
31 15 -1.15509;
36 15 -17.0648;
38 15 -5.58824;
39 15 31.8704;
40 15 -9.78427;
6 16 -0.0465791;
7 16 0.371828;
8 16 -0.325249;
15 16 -379.651;
16 16 1131.92;
17 16 -750.073;
30 16 -1.15509;
31 16 2.77221;
32 16 -1.61712;
39 16 -9.78427;
40 16 23.1242;
41 16 -13.698;
7 17 -0.325249;
8 17 0.844105;
9 17 -0.518855;
11 17 -1024;
16 17 -750.073;
17 17 1914.92;
18 17 -138.499;
31 17 -1.61712;
32 17 2.80473;
33 17 -1.1876;
35 17 -16;
40 17 -13.698;
41 17 35.2181;
42 17 -5.97513;
4 18 -0.324515;
8 18 -0.518855;
9 18 0.84337;
13 18 -535.137;
17 18 -138.499;
18 18 676.012;
28 18 -1.36519;
32 18 -1.1876;
33 18 2.55279;
37 18 -11.6041;
41 18 -5.97513;
42 18 17.0972;
19 19 1.88667;
25 19 -1;
20 20 1.54931;
26 20 -1;
21 21 1.78346;
27 21 -1;
22 22 0.666667;
34 22 -1;
23 23 0.666667;
35 23 -1;
24 24 0.666667;
36 24 -1;
1 25 17.3611;
4 25 -17.3611;
19 25 -1;
2 26 16;
8 26 -16;
20 26 -1;
3 27 17.0648;
6 27 -17.0648;
21 27 -1;
1 28 -17.3611;
4 28 39.4759;
5 28 -10.5107;
9 28 -11.6041;
13 28 3.30738;
14 28 -1.94219;
18 28 -1.36519;
4 29 -10.5107;
5 29 16.0989;
6 29 -5.58824;
13 29 -1.94219;
14 29 3.2242;
15 29 -1.28201;
3 30 -17.0648;
5 30 -5.58824;
6 30 32.4374;
7 30 -9.78427;
14 30 -1.28201;
15 30 2.4371;
16 30 -1.15509;
6 31 -9.78427;
7 31 23.4822;
8 31 -13.698;
15 31 -1.15509;
16 31 2.77221;
17 31 -1.61712;
2 32 -16;
7 32 -13.698;
8 32 35.6731;
9 32 -5.97513;
16 32 -1.61712;
17 32 2.80473;
18 32 -1.1876;
4 33 -11.6041;
8 33 -5.97513;
9 33 17.5792;
13 33 -1.36519;
17 33 -1.1876;
18 33 2.55279;
10 34 17.3611;
13 34 -17.3611;
22 34 -1;
11 35 16;
17 35 -16;
23 35 -1;
12 36 17.0648;
15 36 -17.0648;
24 36 -1;
4 37 -3.30738;
5 37 1.94219;
9 37 1.36519;
10 37 -17.3611;
13 37 39.1419;
14 37 -10.5107;
18 37 -11.6041;
4 38 1.94219;
5 38 -3.2242;
6 38 1.28201;
13 38 -10.5107;
14 38 15.5829;
15 38 -5.58824;
5 39 1.28201;
6 39 -2.4371;
7 39 1.15509;
12 39 -17.0648;
14 39 -5.58824;
15 39 31.8704;
16 39 -9.78427;
6 40 1.15509;
7 40 -2.77221;
8 40 1.61712;
15 40 -9.78427;
16 40 23.1242;
17 40 -13.698;
7 41 1.61712;
8 41 -2.80473;
9 41 1.1876;
11 41 -16;
16 41 -13.698;
17 41 35.2181;
18 41 -5.97513;
4 42 1.36519;
8 42 1.1876;
9 42 -2.55279;
13 42 -11.6041;
17 42 -5.97513;
18 42 17.0972;
1 43 1;
];
A = sparse(ijs(:, 1), ijs(:, 2), ijs(:, 3));
b = [
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
0;
-0.00896054;
-0.0617829;
-0.0772931;
-0.0230638;
-0.0185934;
-0.02;
-0.336;
-0.2755;
-0.353;
0;
0;
0;
1.3;
1.55;
1.4;
0;
-0.9;
0;
-1;
0;
-1.25;
0;
0;
0;
0.167;
-0.042;
0.2835;
-0.171;
0.2275;
-0.259;
0;
];
% ex = [ %% for original symmetrical system
% 0;
% 0.04612219791119214;
% 0.0509334351882598;
% -0.05953571031927305;
% -0.09461814898578046;
% -0.008909854578010561;
% -0.05785829019394401;
% -0.02232729212460287;
% -0.1137760871247425;
% -0.03062777824802364;
% -0.01013282572376477;
% -0.005330939680091628;
% -0.02914165388753019;
% -0.03376073204420303;
% 4.021341450281111e-05;
% -0.01727289094763518;
% -0.008382063634320435;
% -0.04854008812629265;
% -0.2663945795760685;
% -0.4548081594272799;
% -0.3787862287965494;
% -0.02580075363496279;
% -0.02801219343110931;
% -0.09165765332863518;
% -0.1665986614487812;
% -0.4291388294822789;
% -0.3225500876094941;
% 3.967864472606993;
% 5.577372159790927;
% 3.762341481664236;
% 5.858342308599034;
% 3.951628532808602;
% 6.471657726723339;
% -0.01720051102355974;
% -0.01867480495813735;
% -0.06110513277164123;
% -0.1239317474796463;
% -0.1848327901217308;
% -0.4283638085291988;
% 0.07640167050820651;
% -0.1319901818980452;
% 0.4366406661538687;
% 0.0007894844305239289;
% ];
A(8, 2) = -500; %% make non-symmetrical
ex = [
0.000000000000000
0.015818764480650
0.028627515055857
-0.066470494209706
-0.106338553472755
-0.029556247483918
-0.080778493974592
-0.046876059940052
-0.126748712178182
-0.032582479109501
-0.010646589107665
-0.006489850319503
-0.030082640379903
-0.034809123585434
-0.001497869375252
-0.018761742104354
-0.009797350675461
-0.049351378784847
-0.145999102975876
-0.546882809268771
-0.407105729011254
-0.043399950168419
-0.013587814915265
-0.085187156417456
0.060547872388504
-0.571791005228199
-0.373056783462411
4.199136375632448
5.730774734397821
3.598555773194044
5.477255481510613
3.440677757696717
6.533433414753445
-0.028933314578930
-0.009058547806115
-0.056791466007356
-0.206286450370091
-0.246526980342321
-0.398303747647950
0.132430861414235
-0.064740631105635
0.368923140091142
-8.288373070379230
];
t = ''''' : ';
x = mplinsolve(A, b, '');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
x = mplinsolve(full(A), b, '');
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
t = '\ : ';
x = mplinsolve(A, b, '\');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
x = mplinsolve(full(A), b, '\');
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
t = '\ (transpose) : ';
opt = struct('tr', 1);
x = mplinsolve(A', b, '\', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
x = mplinsolve(full(A'), b, '\', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
t = 'LU : ';
x = mplinsolve(A, b, 'LU');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
x = mplinsolve(full(A), b, 'LU');
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'LU (transpose) : ';
opt = struct('tr', 1);
x = mplinsolve(A', b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
x = mplinsolve(full(A'), b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'LU3 : ';
x = mplinsolve(A, b, 'LU3');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
x = mplinsolve(full(A), b, 'LU3');
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'LU, nout = 3, vec = 1, thresh = 1 : ';
opt = struct('nout', 3, 'vec', 1, 'thresh', 1);
x = mplinsolve(A, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
x = mplinsolve(full(A), b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'LU3a : ';
x = mplinsolve(A, b, 'LU3a');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
x = mplinsolve(full(A), b, 'LU3a');
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'LU, nout = 3, vec = 1 : ';
opt = struct('nout', 3, 'vec', 1);
x = mplinsolve(A, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
x = mplinsolve(full(A), b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'LU4 : ';
x = mplinsolve(A, b, 'LU4');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'LU, nout = 4, vec = 1 : ';
opt = struct('nout', 4, 'vec', 1);
x = mplinsolve(A, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'LU5 : ';
x = mplinsolve(A, b, 'LU5');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'LU, nout = 5, vec = 1 : ';
opt = struct('nout', 5, 'vec', 1);
x = mplinsolve(A, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'LU3m : ';
x = mplinsolve(A, b, 'LU3m');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
x = mplinsolve(full(A), b, 'LU3m');
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'LU, nout = 3, vec = 0, thresh = 1 : ';
opt = struct('nout', 3, 'vec', 0, 'thresh', 1);
x = mplinsolve(A, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
x = mplinsolve(full(A), b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'LU3am : ';
x = mplinsolve(A, b, 'LU3am');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
x = mplinsolve(full(A), b, 'LU3am');
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'LU, nout = 3, vec = 0 : ';
opt = struct('nout', 3, 'vec', 0);
x = mplinsolve(A, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
x = mplinsolve(full(A), b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'LU4m : ';
x = mplinsolve(A, b, 'LU4m');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'LU, nout = 4, vec = 0 : ';
opt = struct('nout', 4, 'vec', 0);
x = mplinsolve(A, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'LU5m : ';
x = mplinsolve(A, b, 'LU5m');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'LU, nout = 5, vec = 0 : ';
opt = struct('nout', 5, 'vec', 0);
x = mplinsolve(A, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
%%----- repeat all LU tests with saved factors -----
t = 'pre-factored LU : ';
f = mplinsolve(A);
x = mplinsolve(f, b);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
f = mplinsolve(full(A));
x = mplinsolve(f, b);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'pre-factored LU3 : ';
f = mplinsolve(A, [], 'LU3');
x = mplinsolve(f, b, 'LU3');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
f = mplinsolve(full(A), [], 'LU3');
x = mplinsolve(f, b, 'LU3');
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'pre-factored LU, nout = 3, vec = 1, thresh = 1 : ';
opt = struct('nout', 3, 'vec', 1, 'thresh', 1);
[x, f] = mplinsolve(A, b, 'LU', opt);
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
opt = struct('nout', 3, 'vec', 1, 'thresh', 1);
[x, f] = mplinsolve(full(A), b, 'LU', opt);
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'pre-factored LU3a : ';
[x1, f] = mplinsolve(A, b, 'LU3a');
x = mplinsolve(f, b, 'LU3a');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
[x1, f] = mplinsolve(full(A), b, 'LU3a');
x = mplinsolve(f, b, 'LU3a');
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'pre-factored LU, nout = 3, vec = 1 : ';
opt = struct('nout', 3, 'vec', 1);
f = mplinsolve(A, [], 'LU', opt);
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
opt = struct('nout', 3, 'vec', 1);
f = mplinsolve(full(A), [], 'LU', opt);
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'pre-factored LU4 : ';
[x, f] = mplinsolve(A, b, 'LU4');
x = mplinsolve(f, b, 'LU4');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'pre-factored LU, nout = 4, vec = 1 : ';
opt = struct('nout', 4, 'vec', 1);
f = mplinsolve(A, [], 'LU', opt);
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'pre-factored LU5 : ';
f = mplinsolve(A, [], 'LU5');
x = mplinsolve(f, b, 'LU5');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'pre-factored LU, nout = 5, vec = 1 : ';
opt = struct('nout', 5, 'vec', 1);
[x, f] = mplinsolve(A, b, 'LU', opt);
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'pre-factored LU3m : ';
f = mplinsolve(A, [], 'LU3m');
x = mplinsolve(f, b, 'LU3m');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
f = mplinsolve(full(A), [], 'LU3m');
x = mplinsolve(f, b, 'LU3m');
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'pre-factored LU, nout = 3, vec = 0, thresh = 1 : ';
opt = struct('nout', 3, 'vec', 0, 'thresh', 1);
[x, f] = mplinsolve(A, b, 'LU', opt);
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
opt = struct('nout', 3, 'vec', 0, 'thresh', 1);
f = mplinsolve(full(A), [], 'LU', opt);
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'pre-factored LU3am : ';
f = mplinsolve(A, [], 'LU3am');
x = mplinsolve(f, b, 'LU3am');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
f = mplinsolve(full(A), [], 'LU3am');
x = mplinsolve(f, b, 'LU3am');
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'pre-factored LU, nout = 3, vec = 0 : ';
opt = struct('nout', 3, 'vec', 0);
f = mplinsolve(A, [], 'LU', opt);
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
opt = struct('nout', 3, 'vec', 0);
[x, f] = mplinsolve(full(A), b, 'LU', opt);
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'pre-factored LU4m : ';
[x1, f] = mplinsolve(A, b, 'LU4m');
x = mplinsolve(f, b, 'LU4m');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'pre-factored LU, nout = 4, vec = 0 : ';
opt = struct('nout', 4, 'vec', 0);
f = mplinsolve(A, [], 'LU', opt);
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'pre-factored LU5m : ';
f = mplinsolve(A, [], 'LU5m');
x = mplinsolve(f, b, 'LU5m');
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'pre-factored LU, nout = 5, vec = 0 : ';
opt = struct('nout', 5, 'vec', 0);
[x, f] = mplinsolve(A, b, 'LU', opt);
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
%%----- repeat all LU tests with saved factors AND transpose -----
t = 'transposed LU : ';
f = mplinsolve(A');
x = mplinsolve(f, b, 'LU', struct('tr', 1));
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
f = mplinsolve(full(A'));
x = mplinsolve(f, b, 'LU', struct('tr', 1));
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'transposed LU3 : ';
f = mplinsolve(A', [], 'LU3');
x = mplinsolve(f, b, 'LU3', struct('tr', 1));
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
[x1, f] = mplinsolve(full(A'), b, 'LU3');
x = mplinsolve(f, b, 'LU3', struct('tr', 1));
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'transposed LU, nout = 3, vec = 1, thresh = 1 : ';
opt = struct('nout', 3, 'vec', 1, 'thresh', 1);
[x, f] = mplinsolve(A', b, 'LU', opt);
opt.tr = 1;
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
opt = struct('nout', 3, 'vec', 1, 'thresh', 1);
[x, f] = mplinsolve(full(A'), b, 'LU', opt);
opt.tr = 1;
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'transposed LU3a : ';
f = mplinsolve(A', [], 'LU3a');
x = mplinsolve(f, b, 'LU3a', struct('tr', 1));
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
f = mplinsolve(full(A'), [], 'LU3a');
x = mplinsolve(f, b, 'LU3a', struct('tr', 1));
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'transposed LU, nout = 3, vec = 1 : ';
opt = struct('nout', 3, 'vec', 1);
f = mplinsolve(A', [], 'LU', opt);
opt.tr = 1;
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
opt = struct('nout', 3, 'vec', 1);
[x, f] = mplinsolve(full(A'), b, 'LU', opt);
opt.tr = 1;
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'transposed LU4 : ';
[x1, f] = mplinsolve(A', b, 'LU4');
x = mplinsolve(f, b, 'LU4', struct('tr', 1));
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'transposed LU, nout = 4, vec = 1 : ';
opt = struct('nout', 4, 'vec', 1);
f = mplinsolve(A', [], 'LU', opt);
opt.tr = 1;
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'transposed LU5 : ';
f = mplinsolve(A', [], 'LU5');
x = mplinsolve(f, b, 'LU5', struct('tr', 1));
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'transposed LU, nout = 5, vec = 1 : ';
opt = struct('nout', 5, 'vec', 1);
f = mplinsolve(A', [], 'LU', opt);
opt.tr = 1;
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'transposed LU3m : ';
[x1, f] = mplinsolve(A', b, 'LU3m');
x = mplinsolve(f, b, 'LU3m', struct('tr', 1));
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
f = mplinsolve(full(A'), [], 'LU3m');
x = mplinsolve(f, b, 'LU3m', struct('tr', 1));
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'transposed LU, nout = 3, vec = 0, thresh = 1 : ';
opt = struct('nout', 3, 'vec', 0, 'thresh', 1);
f = mplinsolve(A', [], 'LU', opt);
opt.tr = 1;
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
opt = struct('nout', 3, 'vec', 0, 'thresh', 1);
[x, f] = mplinsolve(full(A'), b, 'LU', opt);
opt.tr = 1;
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'transposed LU3am : ';
[x1, f] = mplinsolve(A', b, 'LU3am');
x = mplinsolve(f, b, 'LU3am', struct('tr', 1));
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
f = mplinsolve(full(A'), [], 'LU3am');
x = mplinsolve(f, b, 'LU3am', struct('tr', 1));
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'transposed LU, nout = 3, vec = 0 : ';
opt = struct('nout', 3, 'vec', 0);
f = mplinsolve(A', [], 'LU', opt);
opt.tr = 1;
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
if skipcrash
t_skip(2, [t 'potential MATLAB crash with non-sparse A']);
else
opt = struct('nout', 3, 'vec', 0);
f = mplinsolve(full(A'), [], 'LU', opt);
opt.tr = 1;
x = mplinsolve(f, b, 'LU', opt);
t_is(x, ex, 12, [t 'x (full A)']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x|| (full A)']);
end
t = 'transposed LU4m : ';
f = mplinsolve(A', [], 'LU4m');
x = mplinsolve(f, b, 'LU4m', struct('tr', 1));
t_is(x, ex, 12, [t 'x']);
t_is(norm(b - A*x), 0, 12, [t '||b - A*x||']);
t = 'transposed LU, nout = 4, vec = 0 : ';