numpy - why np.multiply.reduce([], axis=None) results in 1? - numpy

Question

Why multiply & reduce non-existing element in an empty array-like results in 1?
np.multiply.reduce([], axis=None)
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1

Answer 1

ufunc may have an identify attribute:
In [200]: np.multiply.identity
Out[200]: 1
In [201]: np.multiply.reduce([])
Out[201]: 1.0
which can be replaced in a reduce:
In [202]: np.multiply.reduce([], initial=10)
Out[202]: 10.0
In [203]: np.multiply.reduce([1,2,3], initial=10)
Out[203]: 60
In [204]: np.multiply.reduce([1,2,3], initial=None)
Out[204]: 6
and if None,it can produce an error:
In [205]: np.multiply.reduce([], initial=None)
Traceback (most recent call last):
File "<ipython-input-205-1c3b1c890fd6>", line 1, in <module>
np.multiply.reduce([], initial=None)
ValueError: zero-size array to reduction operation multiply which has no identity
max is a ufunc without an intial:
In [211]: np.max([])
Traceback (most recent call last):
File "<ipython-input-211-93f3814168a1>", line 1, in <module>
np.max([])
File "<__array_function__ internals>", line 5, in amax
File "/usr/local/lib/python3.8/dist-packages/numpy/core/fromnumeric.py", line 2733, in amax
return _wrapreduction(a, np.maximum, 'max', axis, None, out,
File "/usr/local/lib/python3.8/dist-packages/numpy/core/fromnumeric.py", line 87, in _wrapreduction
return ufunc.reduce(obj, axis, dtype, out, **passkwargs)
ValueError: zero-size array to reduction operation maximum which has no identity
In [212]: np.max([], initial=-1)
Out[212]: -1.0
Python reduce
In [222]: from functools import reduce
In [223]: reduce?
Docstring:
reduce(function, sequence[, initial]) -> value
Apply a function of two arguments cumulatively to the items of a sequence,
from left to right, so as to reduce the sequence to a single value.
For example, reduce(lambda x, y: x+y, [1, 2, 3, 4, 5]) calculates
((((1+2)+3)+4)+5). If initial is present, it is placed before the items
of the sequence in the calculation, and serves as a default when the
sequence is empty.
Type: builtin_function_or_method
So with a multiply lambda:
In [224]: reduce(lambda x,y: x*y,[1,2,3])
Out[224]: 6
For a empty list, error is the default behavior:
In [225]: reduce(lambda x,y: x*y,[])
Traceback (most recent call last):
File "<ipython-input-225-780706778563>", line 1, in <module>
reduce(lambda x,y: x*y,[])
TypeError: reduce() of empty sequence with no initial value
But with a supplied initial value:
In [227]: reduce(lambda x,y: x*y,[],1)
Out[227]: 1