numpy.ufunc.reduce#

method

ufunc.reduce(array, axis=0, dtype=None, out=None, keepdims=False, initial=<no value>, where=True)#

Reduces array’s dimension by one, by applying ufunc along one axis.

Let \(array.shape = (N_0, ..., N_i, ..., N_{M-1})\). Then \(ufunc.reduce(array, axis=i)[k_0, ..,k_{i-1}, k_{i+1}, .., k_{M-1}]\) = the result of iterating j over \(range(N_i)\), cumulatively applying ufunc to each \(array[k_0, ..,k_{i-1}, j, k_{i+1}, .., k_{M-1}]\). For a one-dimensional 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:
arrayarray_like

The array to act on.

axisNone 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 well-defined. The ufuncs do not currently raise an exception in this case, but will likely do so in the future.

dtypedata-type code, optional

The data type used to perform the operation. Defaults to that of out if given, and the data type of array otherwise (though upcast to conserve precision for some cases, such as numpy.add.reduce for integer or boolean input).

outndarray, None, or tuple of ndarray and None, optional

A location into which the result is stored. If not provided or None, a freshly-allocated array is returned. For consistency with ufunc.__call__, if given as a keyword, this may be wrapped in a 1-element tuple.

keepdimsbool, 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 array.

initialscalar, 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.

wherearray_like of bool, optional

A boolean array which is broadcasted to match the dimensions of array, 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:
rndarray

The reduced array. If out was supplied, r is a reference to it.

Examples

>>> import numpy as np
>>> np.multiply.reduce([2,3,5])
30

A multi-dimensional 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: zero-size array to reduction operation minimum which has no identity
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