How exactly does the behavior of Python bool and numpy bool_ differ?

There is some confusion with the variables, what is happening is a “confusion” between the module and python, use isinstance(variable, type) to check what is it an if is usable on your code.

Creating a single variable as a bool variable works just fine, python reeds it correctly:

np_bool = np.bool(True)
py_bool = True

print(isinstance(np_bool, bool)) # True
print(isinstance(py_bool, bool)) # True

But with lists it can be different, numpy bool lists are not bool values on a list as you can see in this example:

# Regular list of int
arr0 = [-2, -1, 0, 1, 2]

# Python list of bool
arr1 = [True, False, True, False]

# Numpy list of bool, from int / bool
arr3_a = np.array([-2, -1, 0, 1, 2], dtype=bool)
arr3_b = np.array([True, False, True, False], dtype=bool)

print(isinstance(arr0[0], int))    # True
print(isinstance(arr1[0], bool))   # True

print(isinstance(arr3_a[0], bool)) # False
print(isinstance(arr3_b[0], bool)) # False

In order to use a variable from the numpy list is required a conversion with bool()

arr3_a = np.array([-2, -1, 0, 1, 2], dtype=bool)

x = (bool(arr3_a[0]) is True)
print(isinstance(x, bool)) # True

Quick example of use:

arr3_a = np.array([-2, -1, 0, 1, 2], dtype=bool)

for c in range(0, len(arr3_a)):
    if ( bool(arr3_a[c]) == True ):
        print(("List value {} is True").format(c))
    else:
        print(("List value {} is False").format(c))

Another difference is that automatic casting to integers can be done on np.bool but not on np.bool_.

This is needed, for example, here

>>> np.bool(False) - np.bool(True)
-1

>>> np.bool_(False) - np.bool_(True)
TypeError: numpy boolean subtract, the `-` operator, is not supported, use the bitwise_xor, the `^` operator, or the logical_xor function instead.

Memo

def _test():
    a = np.bool_(True)
    b = np.bool_(True)
    c = np.bool_(False)
    d = np.bool_(False)
    # test_1
    print(a is True)
    print(a is False)
    print(a == True)
    print(a == False)
    print(c is True)
    print(c is False)
    print(c == True)
    print(c == False)
    # test_2
    print(a is b)
    print(a == b)
    print(a and b)
    print(a or b)
    # test_3
    print(a is c)
    print(a == c)
    print(a and c)
    print(a or c)
    # test_4
    print(c is d)
    print(c == d)
    print(c and d)
    print(c or d)
    # test_5
    print(not a)
    print(not c)

test_1:
False
False
True
False
False
False
False
True

test_2:
True
True
True
True

test_3:
False
False
False
True

test_4:
True
True
False
False

test_5:
False
True

Everything here are behaving identically except the ones commented. (extending M.M.’s answer with more details on the comparison of normal boolean behavior vs numpy_boolean behaviour)

  def _test():
    npT1 = np.bool_(True)
    npT2 = np.bool_(True)
    npF1 = np.bool_(False)
    npF2 = np.bool_(False)
    # test_1
    print(npT1 is True)  #npT1 is not python boolean, this will be false
    print(npT1 is False)
    print(npT1 == True)
    print(npT1 == False)
    print(npF1 is True)
    print(npF1 is False)
    print(npF1 == True)
    print(npF1 == False)

    print("vs")

    print(True is True)
    print(True is False)
    print(True == True)
    print(True == False)
    print(npF1 is True)
    print(npF1 is False)
    print(npF1 == True)
    print(npF1 == False)
    
    print("------2----")
    # test_2
    print(npT1 is npT2)
    print(npT1 is npT1)
    print(npT1 == npT2)
    print(npT1 and npT2)
    print(npT1 or npT2)

    print("vs")

    print(True is True)
    print(True is True)
    print(True == True)
    print(True and True)
    print(True or True)
    print("-----3-----")
    # test_3
    print(npT1 is npF1)
    print(npT1 == npF1)
    print(npT1 and npF1)
    print(npT1 or npF1)

    print("vs")

    print(True is False)
    print(True == False)
    print(True and False)
    print(True or False)
    print("-----4-----")
    # test_4
    print(npF1 is npF2)
    print(npF1 == npF2)
    print(npF1 and npF2)
    print(npF1 or npF2)

    print("vs")

    print(False is False)
    print(False == False)
    print(False and False)
    print(False or False)
    print("-----5-----")
    # test_5
    print(not npT1)
    print(not npF1)

    print("vs")

    print(not True)
    print(not False)
    print("-----6-----")
    # test_6
    #print(npF1 - npT1)  ! TypeError: numpy boolean subtract, the `-` operator, is not supported, use the bitwise_xor, the `^` operator, or the logical_xor function instead.
    print(False - True)