‘and’ (boolean) vs ‘&’ (bitwise) – Why difference in behavior with lists vs numpy arrays?

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and tests whether both expressions are logically True while & (when used with True/False values) tests if both are True.

In Python, empty built-in objects are typically treated as logically False while non-empty built-ins are logically True. This facilitates the common use case where you want to do something if a list is empty and something else if the list is not. Note that this means that the list [False] is logically True:

>>> if [False]:
...    print 'True'
...
True

So in Example 1, the first list is non-empty and therefore logically True, so the truth value of the and is the same as that of the second list. (In our case, the second list is non-empty and therefore logically True, but identifying that would require an unnecessary step of calculation.)

For example 2, lists cannot meaningfully be combined in a bitwise fashion because they can contain arbitrary unlike elements. Things that can be combined bitwise include: Trues and Falses, integers.

NumPy objects, by contrast, support vectorized calculations. That is, they let you perform the same operations on multiple pieces of data.

Example 3 fails because NumPy arrays (of length > 1) have no truth value as this prevents vector-based logic confusion.

Example 4 is simply a vectorized bit and operation.

Bottom Line

  • If you are not dealing with arrays and are not performing math manipulations of integers, you probably want and.

  • If you have vectors of truth values that you wish to combine, use numpy with &.

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