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compphys/exo3/test_lu.m
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test_lu.m
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% This script tests lu_decomposition.m
fprintf('Test 1: Identity matrix ...');
for n=1:1:10
A=eye(n);
[l u p]=lu_decomposition(A);
delta=p*A-l*u;
assert(trace(delta'*delta)<1e-10 && trace(triu(l,1)'*triu(l,1)) <1e-10 && trace(tril(u,-1)'*tril(u,-1)) <1e-10 );
end
fprintf('\tpassed\n');
fprintf('Test2 ...')
A=[1 2 3 4; 5 6 7 8; 6 8 10 9; 11 12 15 14];
[l u p]=lu_decomposition(A);
delta=p*A-l*u;
assert(trace(delta'*delta)<1e-10 && trace(triu(l,1)'*triu(l,1)) <1e-10 && trace(tril(u,-1)'*tril(u,-1)) <1e-10 );
fprintf('\tpassed\n');
fprintf('Test 3: Random real matrices ...')
for n=1:1:10
A=rand(n);
[l u p]=lu_decomposition(A);
delta=p*A-l*u;
assert(trace(delta'*delta)<1e-10 && trace(triu(l,1)'*triu(l,1)) <1e-10 && trace(tril(u,-1)'*tril(u,-1)) <1e-10 );
end
fprintf('\tpassed\n');
fprintf('Test 4: Random complex matrices ...')
for n=1:1:10
A=rand(n)+1i*rand(n);
[l u p]=lu_decomposition(A);
delta=p*A-l*u;
assert(trace(delta'*delta)<1e-10 && trace(triu(l,1)'*triu(l,1)) <1e-10 && trace(tril(u,-1)'*tril(u,-1)) <1e-10 );
end
fprintf('\tpassed\n')
fprintf('All tests passed!\n');
fprintf('Pivoting test...\n');
A = [1, 2, 3;
2, 4, 9;
4, -3, 1];
[l u] = lu_nopivoting(A);
l
u
[l u p] = lu_decomposition(A);
l
u
p
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