# How to perform element-wise Boolean operations on NumPy arrays

## Question:

For example, I would like to create a mask that masks elements with value between 40 and 60:

```
foo = np.asanyarray(range(100))
mask = (foo < 40).__or__(foo > 60)
```

Which just looks ugly. I can’t write

```
(foo < 40) or (foo > 60)
```

because I end up with:

```
ValueError Traceback (most recent call last)
...
----> 1 (foo < 40) or (foo > 60)
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()
```

Is there a canonical way of doing element-wise Boolean operations on NumPy arrays with good looking code?

## Answers:

Try this:

```
mask = (foo < 40) | (foo > 60)
```

Note: the `__or__`

method in an object overloads the bitwise or operator (`|`

), not the Boolean `or`

operator.

If you have comparisons within only Booleans, as in your example, you can use the bitwise OR operator `|`

as suggested by Jcollado. But beware, this can give you strange results if you ever use non-Booleans, such as `mask = (foo < 40) | override`

. Only as long as `override`

guaranteed to be either False, True, 1, or 0, are you fine.

More general is the use of NumPy’s comparison set operators, `np.any`

and `np.all`

. This snippet returns all values between 35 and 45 which are less than 40 or not a multiple of 3:

```
import numpy as np
foo = np.arange(35, 46)
mask = np.any([(foo < 40), (foo % 3)], axis=0)
print foo[mask]
OUTPUT: array([35, 36, 37, 38, 39, 40, 41, 43, 44])
```

It is not as nice as with `|`

, but nicer than the code in your question.

Note that you can use `~`

for elementwise negation.

```
arr = np.array([False, True])
~arr
OUTPUT: array([ True, False], dtype=bool)
```

Also `&`

does elementwise *and*

```
arr_1 = np.array([False, False, True, True])
arr_2 = np.array([False, True, False, True])
arr_1 & arr_2
OUTPUT: array([False, False, False, True], dtype=bool)
```

These also work with *Pandas* Series

```
ser_1 = pd.Series([False, False, True, True])
ser_2 = pd.Series([False, True, False, True])
ser_1 & ser_2
OUTPUT:
0 False
1 False
2 False
3 True
dtype: bool
```

You can use the NumPy logical operations. In your example:

```
np.logical_or(foo < 40, foo > 60)
```