Problem
The most common scenario in which we arrive at the problem mentioned is as follows. We start with a numpy array, x
, we wish to select from x
elements that satisfy ceratin conditions, say x > 2 and x < 5
. But trying this out, it does not work, lets see this in code
import numpy as np
# define our numpy array
x = np.array([1,2,3,4,5])
# now try to select elements > 2 and < 5 (so we want 3,4)
x[x > 2 and x < 5]
Running this we arrive at this error, informing us that the truth value of an array with more than one element is ambigeous, we get the same error if we use the or
operator instead of the and
operator
ValueError Traceback (most recent call last)
~\AppData\Local\Temp/ipykernel_9744/1541067368.py in
5
6 # now try to select elements > 2 and < 5 (so we want 3,4)
----> 7 x[x > 2 and x < 5]
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()
Using and/or operators on arrays with more than one element gives an error
Now, lets try to solve this problem, our solution will present two key ideas, the usage of binary operators &
,|
as well as numpy methods .any()
and .all()
. This will be a good reminder on the difference between &
and and
operators, and the |
and or
operators, although they can be used interchangably for one-element variables, their behaviour might differ for variables with more than one element.
Solution
Our solution has two steps. Lets consider the boolean expression x > 2 and x < 5
in detail. First we want to compute (x > 2)
, this returns a boolean array of True
where an element is greater than 2, and False
where an element is less than or equal to 2, lets try this in code
print(x > 2)
print(x < 5)
As expected, for each condition, we get a True
in the position of elements satisfying condition and False
otherwise, For example, for x = [1,2,3,4,5]
and condition x>2
, first 2 elements fail the condition, and last 3 elements pass the condition, so we get [False False True True True]
, the following is our ouptu after running the 2 lines of code above
[False False True True True]
[ True True True True False]
Next we have either one of two choices. If we want to specify elements satisfying conditions using indexes, then we want to perform element-wise operations. Hence, for and
we resort to either &
operator or the np.logical_and()
method. For or
we can use |
operator or np.logical_or
method. So again lets try to select elements satisfying x > 2 and x < 5
print(x[(x > 2) & (x < 5)])
print(x[np.logical_and(x > 2,x < 5)])
Notice how when using the &
operator, we need to use ()
, since the &
operator takes precedence over the > and < operators. Running the code above we get our two desired elements satisfying the conditions, 3,4
The & operator takes precedence over the > , < operators, so use of () is necessary
[3 4]
[3 4]
Use & or np.logical_and() for element-wise and operation on arrays with more than one element
We can repeat the same code again for or, using either the |
operator or np.logical_or
method
Use | or np.logical_or() for element-wise or operation on arrays with more than one element
Now what if our original goal was to get a single boolean value? Just either True
, if there is any element satisfying this condition or False
otherwise. Or what if we want a single boolean value which is True
if all elements satisfy the condition and Falase
otherwise? This is when we can add the .any()
and .all()
methods to the above code.
print(((x > 2) & (x < 5)).any())
print(np.logical_and(x > 2,x < 5).all())
In the above code, we can use &
and np.logical_and()
interchangeably. When using the .any()
function we expect the result to be True
since some elements like 3,4
satisfy the condition. However when using the .all()
method, we expect the result to be False
since not all elements satisfy the condition like 1,5
, Here is the output of the above code
True
False
Use .all() to AND all values of an array into a single boolean value
Use .any() to OR all values of an array into a single boolean value
Conclusion
This was a quick guide on how to solve the The truth value of an array with more than one element is ambiguous. use a.any() or a.all() problem, which is an error we face when trying to apply logical operators on arrays with more than one element. We saw how we can use the &
and |
operators or interchangeably the np.logical_and()
and np.logical_or()
methods to perform element-wise logic operations on elements, hence getting indexes of elements satisfying the condition. We also saw how we can use the .any()
or .all()
methods to obtain a single boolean value out of an array of boolean values