numpy.ufunc.reduce¶

ufunc.
reduce
(a, axis=0, dtype=None, out=None, keepdims=False, initial)¶ Reduces a’s dimension by one, by applying ufunc along one axis.
Let a.shape = (N_0, ..., N_i, ..., N_{M1}). Then ufunc.reduce(a, axis=i)[k_0, ..,k_{i1}, k_{i+1}, .., k_{M1}] = the result of iterating j over range(N_i), cumulatively applying ufunc to each a[k_0, ..,k_{i1}, j, k_{i+1}, .., k_{M1}]. 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.
New in version 1.7.0.
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.
New in version 1.7.0.
 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.New in version 1.15.0.
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.>>> np.add.reduce([10], initial=5) 15 >>> np.add.reduce(np.ones((2, 2, 2)), axis=(0, 2), initializer=10) array([14., 14.])
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([]) Traceback (most recent call last): ... ValueError: zerosize array to reduction operation minimum which has no identity