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function test3
%TEST3 test cs_lsolve, cs_ltsolve, cs_usolve, cs_chol
%
% Example:
% test3
% See also: testall
% CXSparse, Copyright (c) 2006-2022, Timothy A. Davis. All Rights Reserved.
% SPDX-License-Identifier: LGPL-2.1+
clear
index = ssget ;
[ignore f] = sort (max (index.nrows, index.ncols)) ;
f = f (1:100) ;
clf
% f = f(1)
for i = f
Prob = ssget (i) ;
disp (Prob) ;
for cmplex = 0:double(~ispc)
A = Prob.A ;
[m n] = size (A) ;
if (m ~= n)
continue
end
if (cmplex)
A = A + 1i*sprand(A) ;
end
A = A*A' + 2*n*speye (n) ;
try
p = amd (A) ;
catch
p = symamd (A) ;
end
try
L0 = chol (A)' ;
catch
continue
end
b = rand (n,1) ;
if (~ispc)
if (mod (i,2) == 1)
b = b + 1i*rand(n,1) ;
end
end
C = A(p,p) ;
c = condest (C) ;
fprintf ('condest: %g\n', c) ;
x1 = L0\b ;
x2 = cs_lsolve (L0,b) ;
err = norm (x1-x2,1) ;
if (err > 1e-12 * c)
error ('!') ;
end
x1 = L0'\b ;
x2 = cs_ltsolve (L0,b) ;
err = norm (x1-x2,1) ;
if (err > 1e-10 * c)
error ('!') ;
end
U = L0' ;
x1 = U\b ;
x2 = cs_usolve (U,b) ;
err = norm (x1-x2,1) ;
if (err > 1e-10 * c)
error ('!') ;
end
L2 = cs_chol (A) ;
subplot (2,3,1) ; spy (L0) ;
subplot (2,3,4) ; spy (L2) ;
err = norm (L0-L2,1) ;
if (err > 1e-8 * c)
error ('!') ;
end
L1 = chol (C)' ;
L2 = cs_chol (C) ;
subplot (2,3,2) ; spy (L1) ;
subplot (2,3,5) ; spy (L2) ;
err = norm (L1-L2,1) ;
if (err > 1e-8 * c)
error ('!') ;
end
[L3,p] = cs_chol (A) ;
C = A(p,p) ;
L4 = chol (C)' ;
subplot (2,3,3) ; spy (L4) ;
subplot (2,3,6) ; spy (L3) ;
err = norm (L4-L3,1) ;
if (err > 1e-8 * c)
error ('!') ;
end
drawnow
end
end
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