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% UMFPACK_TEST: test UMFPACK solve: b/A, A\b with iterative refinement
% Requires the UFsparse package for downloading matrices from the UF
% sparse matrix library.
%
% UMFPACK Version 4.4, Copyright (c) 2005 by Timothy A. Davis.
% All Rights Reserved. Type umfpack_details for License.
index = UFget ;
f = find (index.nrows == index.ncols) ;
[ignore, i] = sort (index.nrows (f)) ;
f = f (i) ;
Control = umfpack ;
Control (1) = 0 ;
warning ('off', 'all') ;
figure (1)
clf
for i = f
fprintf ('\nmatrix: %s %s %d\n', index.Group{i}, index.Name{i}, index.nrows(i)) ;
Prob = UFget (i) ;
A = Prob.A ;
n = size (A,1) ;
b = rand (1,n) ;
c = b' ;
try
%-----------------------------------------------------------------------
% symbolic factorization
%-----------------------------------------------------------------------
[P1, Q1, Fr, Ch, Info] = umfpack (A, 'symbolic') ;
subplot (2,2,1)
spy (A)
title ('A')
subplot (2,2,2)
treeplot (Fr (1:end-1,2)') ;
title ('supercolumn etree')
%-----------------------------------------------------------------------
% P(R\A)Q = LU
%-----------------------------------------------------------------------
[L,U,P,Q,R,Info] = umfpack (A) ;
err = lu_normest (P*(R\A)*Q, L, U) ;
fprintf ('norm est PR\\AQ-LU: %g relative: %g\n', ...
err, err / norm (A,1)) ;
subplot (2,2,3)
spy (P*A*Q)
title ('PAQ') ;
cs = Info (57) ;
rs = Info (58) ;
subplot (2,2,4)
hold off
spy (L|U)
hold on
if (cs > 0)
plot ([0 cs n n 0] + .5, [0 cs cs 0 0]+.5, 'c') ;
end
if (rs > 0)
plot ([0 rs rs 0 0] + cs +.5, [cs cs+rs n n cs]+.5, 'r') ;
end
title ('LU factors')
drawnow
%-----------------------------------------------------------------------
% PAQ = LU
%-----------------------------------------------------------------------
[L,U,P,Q] = umfpack (A) ;
err = lu_normest (P*A*Q, L, U) ;
fprintf ('norm est PAQ-LU: %g relative: %g\n', ...
err, err / norm (A,1)) ;
%-----------------------------------------------------------------------
% solve
%-----------------------------------------------------------------------
x1 = b/A ;
y1 = A\c ;
m1 = norm (b-x1*A) ;
m2 = norm (A*y1-c) ;
% factor the transpose
Control (8) = 2 ;
[x, info] = umfpack (A', '\', c, Control) ;
lunz0 = info (44) + info (45) - info (67) ;
r = norm (A'*x-c) ;
fprintf (':: %8.2e matlab: %8.2e %8.2e\n', r, m1, m2) ;
% factor the original matrix and solve xA=b
for ir = 0:4
Control (8) = ir ;
[x, info] = umfpack (b, '/', A, Control) ;
r = norm (b-x*A) ;
if (ir == 0)
lunz1 = info (44) + info (45) - info (67) ;
end
fprintf ('%d: %8.2e %d %d\n', ir, r, info (81), info (82)) ;
end
% factor the original matrix and solve Ax=b
for ir = 0:4
Control (8) = ir ;
[x, info] = umfpack (A, '\', c, Control) ;
r = norm (A*x-c) ;
fprintf ('%d: %8.2e %d %d\n', ir, r, info (81), info (82)) ;
end
fprintf ('lunz trans %12d no trans: %12d trans/notrans: %10.4f\n', ...
lunz0, lunz1, lunz0 / lunz1) ;
%-----------------------------------------------------------------------
% get the determinant
%-----------------------------------------------------------------------
det1 = det (A) ;
det2 = umfpack (A, 'det') ;
[det3 dexp3] = umfpack (A, 'det') ;
err = abs (det1-det2) ;
err3 = abs (det1 - (det3 * 10^dexp3)) ;
denom = det1 ;
if (denom == 0)
denom = 1 ;
end
err = err / denom ;
err3 = err3 / denom ;
fprintf ('det: %24.16e + (%24.16e)i MATLAB\n', real(det1), imag(det1)) ;
fprintf ('det: %24.16e + (%24.16e)i umfpack\n',real(det2), imag(det2)) ;
fprintf ('det: (%24.16e + (%24.16e)i) * 10^(%g) umfpack\n', real(det3), imag(det3), dexp3) ;
fprintf ('diff %g %g\n', err, err3) ;
catch
fprintf ('failed\n') ;
end
% pause
end
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