Numpy complaining about ambigoous array: ValueError: The truth value of - arrays

Question

I have a minimal code in Python 3, which uses numpy and the function apply_along_axis. I cannot understand the reason I am having this error:
ValueError: The truth value of an array with more than one element is ambiguous. Use a.any() or a.all()
Providing a direct formula inside the lambda is working. As soon as I use another function, I am getting this error. Am I supposed to return something else?
The minimal code:
import numpy as np
def logn(x, b):
return np.log(x)/np.log(b)
def h(x, b):
if x == 0:
return 0
else:
return -x*logn(x, b)
p = np.array([0.00000000e+00, 9.99997956e-01, 2.04440466e-06])
print(np.apply_along_axis(lambda _e: h(_e, 3), -1, p))

Answer 1

Look at what apply_along_axis passes to your function:
In [99]: def foo(x):
...: print(x)
...: return x
...:
In [100]: np.apply_along_axis(foo, -1, p)
[0.00000000e+00 9.99997956e-01 2.04440466e-06]
Out[100]: array([0.00000000e+00, 9.99997956e-01, 2.04440466e-06])
In the case of a 1d array, it passes the whole array at once. It does not iterate on that dimension. That's whole purpose of apply_along_axis - to pass 1d arrays to your function.
Judging from other SO apply_along_axis is not very useful, and often gives problems. It is not faster than a more explicit iteration. For 3d (or higher) it can make the iteration (over the 'other' two axes) simpler (but again not faster).
For the 1d p, this is simpler:
In [102]: [h(_e,3) for _e in p]
Out[102]: [0, 1.8605270777946112e-06, 2.4378506521338855e-05]
A non-iterative approach is to use a boolean mask to select which p are used in the calculation. That way you don't have to use a scalar if expression:
In [106]: mask = p!=0
In [107]: mask
Out[107]: array([False, True, True])
In [108]: p1 = p[mask]
In [109]: res = np.zeros(p.shape)
In [110]: res[mask] = -p1*logn(p1,3)
In [111]: res
Out[111]: array([0.00000000e+00, 1.86052708e-06, 2.43785065e-05])
ufunc like np.log take a where parameter, which can be used to bypass bad input values:
In [114]: -p * np.log(p, where=(p!=0), out=np.zeros(p.shape))/np.log(3)
Out[114]: array([-0.00000000e+00, 1.86052708e-06, 2.43785065e-05])