what causes different in array sum along axis for C versus F ordered arrays in numpy

Question

I am curious if anyone can explain what exactly leads to the discrepancy in this particular handling of C versus Fortran ordered arrays in numpy. See the code

Answer 1

Floating point math isn't necessarily associative, i.e. (a+b)+c != a+(b+c).

Since you're adding along different axes, the order of operations is different, which can affect the final result. As a simple example, consider the matrix whose sum is 1.

a = np.array([[1e100, 1], [-1e100, 0]])
print(a.sum())   # returns 0, the incorrect result
af = np.asfortranarray(a)
print(af.sum())  # prints 1

(Interestingly, a.T.sum() still gives 0, as does aT = a.T; aT.sum() , so I'm not sure how exactly this is implemented in the backend)

The C order is using the sequence of operations (left-to-right) 1e100 + 1 + (-1e100) + 0 whereas the Fortran order uses 1e100 + (-1e100) + 1 + 0. The problem is that (1e100+1) == 1e100 because floats don't have enough precision to represent that small difference, so the 1 gets lost.

In general, don't do equality testing on floating point numbers, instead compare using a small epsilon (if abs(float1 - float2) < 0.00001 or np.isclose). If you need arbitrary float precision, use the Decimal library or fixed-point representation and ints.