python tilde unary operator as negation numpy bool array

Question

Should be a simple question, but I'm unable to find an answer anywhere. The ~ operator in python is a documented as a bitwise inversion operator. Fine. I have noticed seemingly schizophrenic behavior though, to wit:

~True -> -2
~1 -> -2
~False -> -1
~0 -> -1
~numpy.array([True,False],dtype=int) -> array([-2,-1])
~numpy.array([True,False],dtype=bool) -> array([False,True])

In the first 4 examples, I can see that python is implementing (as documented) ~x = -(x+1), with the input treated as an int even if it's boolean. Hence, for a scalar boolean, ~ is not treated as a logical negation. Not that the behavior is identical on a numpy array defined with boolean values by with an int type.

Why does ~ then work as a logical negation operator on a boolean array (Also notice: ~numpy.isfinite(numpy.inf) -> True?)?

It is extremely annoying that I must use not() on a scalar, but not() won't work to negate an array. Then for an array, I must use ~, but ~ won't work to negate a scalar...

Ovid

Answer 1

not is implemented through the __nonzero__ special method, which is required to return either True or False, so it can't give the required result. Instead the ~ operator is used, which is implemented through the __not__ special method. For the same reason, & and | are used in place of and and or.

PEP 335 aimed to allow overloading of boolean operators but was rejected because of excessive overhead (it would e.g. complicate if statements). PEP 225 suggests a general syntax for "elementwise" operators, which would provide a more general solution, but has been deferred. It appears that the current situation, while awkward, is not painful enough to force change.

np.isfinite when called on a scalar returns a value of type np.bool_, not bool. np.bool_ is also the type you get when extracting a scalar value from an array of bool dtype. If you use np.True_ and np.False_ in place of True and False you will get consistent behaviour under ~.

Schaper

Thanks ecatmur for the explanation, and especially for mentioning & and |. I didn't know about those, and had used logical_and and logical_or instead. – Ovid

I am using numpy for ages and till now did not know the purpose of those seemingly redefined-but-underlined constructs like np.False_. This all makes sense now – Junie