Why does my subtraction yield different results?

I have been working on an analysis and after simplifying my code for speed the results came out differently even though I think I should have obtained the same results.

L = eye(n * c) / (eye(n * c) - A);
x_test = L * F * ones(p , 1);
isequal(eps(x),eps(x_test))
% so x and x_test are equal
x_1 = L * F * ones(p , 1) - (eye(n * c) - A_tilde) \ F_tilde * ones(p , 1);
x_2 = x                   - (eye(n * c) - A_tilde) \ F_tilde * ones(p , 1);
isequal(eps(x_1),eps(x_2))

The first isequal return me a one while the second isequal returns me a zero.

This means that x_test is equal to x but if I subtract the same vector on the RHS of the minus sign, I get a different result. I am not sure how this is possible. Could anyone point me in the right direction?

Answer 1

[Matt J]

isequal(eps(x),eps(x_test))=1 does not establish that x=x_test. You misunderstand what eps() does.

eps(1)

ans = 2.2204e-16

eps(1.1)

ans = 2.2204e-16

isequal(eps(1), eps(1.1))

ans = logical
   1

Answer 2

[William Rose]

@Hylke Dijkstra,

Can you provide more of your code? Why do you use the eps() function when testing the equality of two numbers or vectors or matrices? The following example shows that two unequal numbers can have equal eps's.

x1=1; x2=x1+1e-8; isequal(x1,x2), isequal(eps(x1),eps(x2))

ans = logical
   0

ans = logical
   1