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function lintests
%LINTESTS test linfactor with many different kinds of systems.
% Compares x=A\b, linfactor and (ack!) inv(A)*b. You should never, ever use
% inv(A) to solve a linear system.
%
% Example
% lintests
%
% See also lintest, linfactor, mldivide.
% LINFACTOR, Copyright (c) 2008, Timothy A Davis. All Rights Reserved.
% SPDX-License-Identifier: BSD-3-clause
rand ('state', 0) ;
help linfactor
for n = [100 1000 2000]
fprintf ('\nn: %d (with all nonzero matrix A)\n', n) ;
% dense LU
A = rand (n) ;
b = rand (n,1) ;
lintest (A,b) ;
% sparse LU
A = sparse (A) ;
lintest (A,b) ;
% dense Cholesky
A = A*A' + 10*eye(n) ;
lintest (A,b) ;
% sparse Cholesky
A = sparse (A) ;
lintest (A,b) ;
end
for n = [1000 2000]
% note that UMFPACK is not particularly fast for tridiagonal matrices
% (see "doc mldivide", which uses a specialized tridiagonal solver)
fprintf ('\nn: %d (sparse tridiagonal matrix)\n', n) ;
% sparse LU
e = rand (n, 1) ;
b = rand (n, 1) ;
A = spdiags ([e 4*e e], -1:1, n, n) ;
lintest (A,b) ;
% sparse Cholesky
e = ones (n, 1) ;
A = spdiags ([e 4*e e], -1:1, n, n) ;
lintest (A,b) ;
end
% sparse LU again
fprintf ('\nwest0479:\n') ;
load west0479 ;
n = size (west0479, 1) ;
b = rand (n, 1) ;
lintest (west0479, b) ;
% completely break inv(A) with a simple 2-by-2 matrix ...
fprintf ('\nbreak inv(A) with a trivial 2-by-2 matrix:\n') ;
s = warning ('off', 'MATLAB:singularMatrix') ;
lintest (rand(2) * realmin/2, ones(2,1)) ;
warning (s) ;
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