Reduces a
’s dimension by one, by applying ufunc along one axis.
Let . Then = the result of iterating j
over , cumulatively applying ufunc to each . For a onedimensional array, reduce produces results equivalent to:
r = op.identity # op = ufunc
for i in range(len(A)):
r = op(r, A[i])
return r
For example, add.reduce() is equivalent to sum().
Parameters: 

a : array_like 
The array to act on. 
axis : None or int or tuple of ints, optional 
Axis or axes along which a reduction is performed. The default (axis = 0) is perform a reduction over the first dimension of the input array. axis may be negative, in which case it counts from the last to the first axis. If this is None , a reduction is performed over all the axes. If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before. For operations which are either not commutative or not associative, doing a reduction over multiple axes is not welldefined. The ufuncs do not currently raise an exception in this case, but will likely do so in the future. 
dtype : datatype code, optional 
The type used to represent the intermediate results. Defaults to the datatype of the output array if this is provided, or the datatype of the input array if no output array is provided. 
out : ndarray, None, or tuple of ndarray and None, optional 
A location into which the result is stored. If not provided or None , a freshlyallocated array is returned. For consistency with ufunc.__call__ , if given as a keyword, this may be wrapped in a 1element tuple. Changed in version 1.13.0: Tuples are allowed for keyword argument. 
keepdims : bool, optional 
If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr . 
initial : scalar, optional 
The value with which to start the reduction. If the ufunc has no identity or the dtype is object, this defaults to None  otherwise it defaults to ufunc.identity. If None is given, the first element of the reduction is used, and an error is thrown if the reduction is empty. 
where : array_like of bool, optional 
A boolean array which is broadcasted to match the dimensions of a , and selects elements to include in the reduction. Note that for ufuncs like minimum that do not have an identity defined, one has to pass in also initial . 
Returns: 

r : ndarray 
The reduced array. If out was supplied, r is a reference to it. 
Examples
>>> np.multiply.reduce([2,3,5])
30
A multidimensional array example:
>>> X = np.arange(8).reshape((2,2,2))
>>> X
array([[[0, 1],
[2, 3]],
[[4, 5],
[6, 7]]])
>>> np.add.reduce(X, 0)
array([[ 4, 6],
[ 8, 10]])
>>> np.add.reduce(X) # confirm: default axis value is 0
array([[ 4, 6],
[ 8, 10]])
>>> np.add.reduce(X, 1)
array([[ 2, 4],
[10, 12]])
>>> np.add.reduce(X, 2)
array([[ 1, 5],
[ 9, 13]])
You can use the initial
keyword argument to initialize the reduction with a different value, and where
to select specific elements to include:
>>> np.add.reduce([10], initial=5)
15
>>> np.add.reduce(np.ones((2, 2, 2)), axis=(0, 2), initial=10)
array([14., 14.])
>>> a = np.array([10., np.nan, 10])
>>> np.add.reduce(a, where=~np.isnan(a))
20.0
Allows reductions of empty arrays where they would normally fail, i.e. for ufuncs without an identity.
>>> np.minimum.reduce([], initial=np.inf)
inf
>>> np.minimum.reduce([[1., 2.], [3., 4.]], initial=10., where=[True, False])
array([ 1., 10.])
>>> np.minimum.reduce([])
Traceback (most recent call last):
...
ValueError: zerosize array to reduction operation minimum which has no identity