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function test2 (nmat)
%test2: KLU test
% Example:
% test2
% See also klu
% KLU, Copyright (c) 2004-2022, University of Florida. All Rights Reserved.
% Authors: Timothy A. Davis and Ekanathan Palamadai.
% SPDX-License-Identifier: LGPL-2.1+
clear functions
% rand ('state', 0) ;
% warning ('off', 'MATLAB:singularMatrix') ;
% warning ('off', 'MATLAB:nearlySingularMatrix') ;
% warning ('off', 'MATLAB:divideByZero') ;
index = ssget ;
f = find (index.nrows == index.ncols) ;
[ignore i] = sort (index.nnz (f)) ; %#ok
f = f (i) ;
if (nargin < 1)
nmat = 500 ;
end
nmat = min (nmat, length (f)) ;
f = f (1:nmat) ;
if (~isempty (strfind (computer, '64')))
is64 = 1 ;
else
is64 = 0 ;
end
Tklu = 1e-6 * ones (2*nmat,1) ;
Tmatlab = zeros (2*nmat,1) ;
Tcsparse = zeros (2*nmat,1) ;
LUnz = zeros (2*nmat, 1) ;
k = 0 ;
h = waitbar (0, 'KLU test 2 of 5') ;
clf
% try
for kk = 1:nmat
Prob = ssget (f (kk), index) ;
waitbar (kk/nmat, h) ;
disp (Prob) ;
if (isfield (Prob, 'kind'))
if (~isempty (strfind (Prob.kind, 'subsequent')))
fprintf ('skip ...\n') ;
continue
end
end
A = Prob.A ;
for do_complex = 0:1
k = k + 1 ;
if (do_complex)
A = sprand (A) + 1i * sprand (A) ;
end
try
[L,U,p,q] = lu (A, 'vector') ;
catch %#ok
% older version of MATLAB, which doesn't have 'vector' option
[L,U,P,Q] = lu (A) ;
[p ignore1 ignore2] = find (P') ; %#ok
[q ignore1 ignore2] = find (Q) ; %#ok
clear ignore1 ignore2 P Q
end
LU.L = L ;
LU.U = U ;
if (is64)
LU.p = int64 (p) ;
LU.q = int64 (q) ;
else
LU.p = int32 (p) ;
LU.q = int32 (q) ;
end
LUnz (k) = nnz (L) + nnz (U) ;
n = size (A,1) ;
do_klu = (nnz (diag (U)) == n) ;
if (do_klu)
fprintf ('klu...\n') ;
err = 0 ;
erc = 0 ;
er2 = 0 ;
for nrhs = 10:-1:1
b = rand (n,nrhs) ;
tic ;
x = klu (LU,'\',b) ;
Tklu (k) = max (1e-6, toc) ;
tic ;
y = U \ (L \ b (p,:)) ;
y (q,:) = y ;
Tmatlab (k) = max (1e-6, toc) ;
if (nrhs == 1 & isreal (U) & isreal (L) & isreal (b)) %#ok
tic ;
z = cs_usolve (U, cs_lsolve (L, b (p))) ;
z (q) = z ;
Tcsparse (k) = max (1e-6, toc) ;
erc = norm (A*z-b,1) / norm (A,1) ;
end
err = max (err, norm (A*x-b,1) / norm (A,1)) ;
er2 = max (er2, norm (A*y-b,1) / norm (A,1)) ;
if (err > 100*er2)
fprintf ('error %g %g\n', err, er2) ;
error ('?') ;
end
end
fprintf ('klu... with randomized scaling for L\n') ;
er3 = 0 ;
er4 = 0 ;
D = spdiags (rand (n,1), 0, n, n) ;
LU.L = D * L ;
A2 = D * A (p,q) ;
if (is64)
LU.p = int64 (1:n) ;
LU.q = int64 (1:n) ;
else
LU.p = int32 (1:n) ;
LU.q = int32 (1:n) ;
end
for nrhs = 1:10
b = rand (n,nrhs) ;
x = klu (LU,'\',b) ;
y = U \ (LU.L \ b) ;
er3 = max (er3, norm (A2*x-b,1) / norm (A,1)) ;
er4 = max (er4, norm (A2*y-b,1) / norm (A,1)) ;
if (er3 > 1e3*er4)
fprintf ('error %g %g\n', er3, er4) ;
error ('?') ;
end
end
else
err = Inf ;
er2 = Inf ;
erc = Inf ;
end
lumax = max (LUnz (1:k)) ;
if (k > 1)
loglog (...
LUnz (1:k), Tmatlab (1:k) ./ Tklu (1:k), 'o', ...
LUnz (1:k), Tcsparse (1:k) ./ Tklu (1:k), 'x', ...
[20 lumax], [1 1], 'r-') ;
axis ([sort([20 lumax]) .1 20]) ;
drawnow
end
fprintf ('err %g %g %g\n', err, er2, erc) ;
end
end
% catch me
% disp (me.message) ;
% end
close (h) ;
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