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function spqr_demo
%SPQR_DEMO short demo of SuiteSparseQR
%
% Example:
% spqr_demo
%
% See also SPQR, SPQR_SOLVE, SPQR_QMULT, SPQR_MAKE, SPQR_INSTALL.
% SPQR, Copyright (c) 2008-2022, Timothy A Davis. All Rights Reserved.
% SPDX-License-Identifier: GPL-2.0+
help spqr
help spqr_solve
help spqr_qmult
help spqr_demo
% input ('Hit enter to start the SuiteSparseQR demo: ', 's') ;
fprintf ('\nTesting SuiteSparseQR functions ... please wait ...\n') ;
load west0479 ;
A = west0479 ;
rand ('state', 0) ; %#ok
m = size (A,1) ;
clf
maxerr = 0 ;
for acomplex = 0:1
if (acomplex)
A = A + 1i * sprand (A) ;
end
anorm = norm (A,1) ;
R1 = spqr (A) ;
err = norm (R1'*R1 - A'*A, 1) / anorm^2 ;
maxerr = max (maxerr, err) ;
[Q,R,E] = spqr (A) ;
err = norm (Q*R-A*E, 1) / anorm ;
maxerr = max (maxerr, err) ;
[H,R,E] = spqr (A, struct ('Q', 'Householder')) ;
err = norm (spqr_qmult (H,R,1) - A*E, 1) / anorm ;
maxerr = max (maxerr, err) ;
if (acomplex)
subplot (2,5,7) ; spy (R1) ; title ('R, no permutation (complex)') ;
subplot (2,5,8) ; spy (R) ; title ('R with colamd (complex)') ;
subplot (2,5,9) ; spy (Q) ; title ('Q with colamd (complex)') ;
subplot (2,5,10) ; spy (H.H) ; title ('H with colamd (complex)') ;
else
subplot (2,5,1) ; spy (A) ; title ('A') ;
subplot (2,5,2) ; spy (R1) ; title ('R, no permutation') ;
subplot (2,5,3) ; spy (R) ; title ('R with colamd') ;
subplot (2,5,4) ; spy (Q) ; title ('Q with colamd') ;
subplot (2,5,5) ; spy (H.H) ; title ('H with colamd') ;
end
drawnow
% test spqr_solve: real/complex, sparse/full,
% single/multiple right-hand-sides
for bcomplex = 0:1
for bsparse = 0:1
for nrhs = 0:10
if (bsparse)
b = sprand (m, nrhs, 0.1) ;
else
b = rand (m, nrhs) ;
end
if (bcomplex)
b = b + 1i * sprand (b) ;
end
x = spqr_solve (A,b) ;
err = norm (A*x-b,1) / max (anorm * norm(x,1) + norm (b,1), 1) ;
maxerr = max (maxerr, err) ;
end
end
end
end
fprintf ('\nQR maximum error: %g\n\n', maxerr) ;
if (maxerr > 1e-12)
error ('One or more tests failed; error is high!') ;
end
% ------------------------------------------------------------------------------
% compare spqr_solve
% ------------------------------------------------------------------------------
fprintf ('Compare performance with MATLAB on a dense least-squares problem:\n');
A = rand (2000,1000) ;
b = rand (2000,1) ;
S = sparse (A) ;
fprintf ('\nA = rand (2000,1000) ;\nb = rand (2000,1) ;\nS = sparse (A) ;\n') ;
fprintf ('tic, x = spqr_solve(S,b) ; toc ') ;
tic
x = spqr_solve (S, b) ;
t1 = toc ;
r1 = norm (A*x-b,1) ;
r1b = norm (A'*(A*x)-A'*b,1) / norm (A'*A,1) ;
fprintf ('%% time %8.3f residual %8.3e normal eqn resid %8.3e\n', t1,r1, r1b) ;
fprintf ('tic, x = A\\b ; toc ') ;
tic
x = A\b ;
t2 = toc ;
r2 = norm (A*x-b,1) ;
r2b = norm (A'*(A*x)-A'*b,1) / norm (A'*A,1) ;
fprintf ('%% time %8.3f residual %8.3e normal eqn resid %8.3e\n', t2,r2,r2b) ;
fprintf ('tic, x = S\\b ; toc ') ;
tic
x = S\b ;
t3 = toc ;
r3 = norm (A*x-b,1) ;
r3b = norm (A'*(A*x)-A'*b,1) / norm (A'*A,1) ;
fprintf ('%% time %8.3f residual %8.3e normal eqn resid %8.3e\n', t3,r3,r3b) ;
% ------------------------------------------------------------------------------
% compare spqr with 1000-by-2000 system
% ------------------------------------------------------------------------------
fprintf ('\nA = rand (1000,2000) ;\nS = sparse (A) ;\n') ;
A = rand (1000,2000) ;
S = sparse (A) ;
fprintf ('tic, R = spqr(S) ; toc ') ;
tic
R = spqr (S) ;
t1 = toc ;
r1 = norm (R'*R-A'*A,1) / norm(A,1)^2 ;
fprintf ('%% time %8.3f error %8.3e\n', t1,r1) ;
clear R
fprintf ('tic, R = qr(A) ; toc ') ;
tic
R = qr (A) ;
t2 = toc ;
R = triu (R) ;
r2 = norm (R'*R-A'*A,1) / norm(A,1)^2 ;
fprintf ('%% time %8.3f error %8.3e\n', t2,r2) ;
clear R
fprintf ('tic, R = qr(S) ; toc ') ;
tic
R = qr (S) ;
t3 = toc ;
r3 = norm (R'*R-A'*A,1) / norm(A,1)^2 ;
fprintf ('%% time %8.3f error %8.3e\n', t3,r3) ;
clear R
% ------------------------------------------------------------------------------
% compare spqr with 100-by-20000 system
% ------------------------------------------------------------------------------
A = rand (100,20000) ;
S = sparse (A) ;
fprintf ('\nA = rand (100,20000) ;\nS = sparse (A) ;\n') ;
fprintf ('tic, R = spqr(S) ; toc ') ;
tic
R = spqr (S) ; %#ok
t1 = toc ;
fprintf ('%% time %8.3f\n', t1) ;
clear R
fprintf ('tic, R = qr(A) ; toc ') ;
tic
R = qr (A) ; %#ok
t2 = toc ;
fprintf ('%% time %8.3f\n', t2) ;
clear R
% skip the old MATLAB QR ... it's way to slow ...
% fprintf ('tic, R = qr(S) ; toc ') ;
% try
% tic
% R = qr (S) ; %#ok
% t3 = toc ;
% fprintf ('%% time %8.3f\n', t3) ;
% catch %#ok
% fprintf ('%% MATLAB sparse qr failed ...\n') ;
% end
% clear R
fprintf ('All spqr tests passed\n') ;
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