numpy.ufunc.reduceat¶

ufunc.
reduceat
(a, indices, axis=0, dtype=None, out=None)¶ Performs a (local) reduce with specified slices over a single axis.
For i in
range(len(indices))
,reduceat
computesufunc.reduce(a[indices[i]:indices[i+1]])
, which becomes the ith generalized “row” parallel to axis in the final result (i.e., in a 2D array, for example, if axis = 0, it becomes the ith row, but if axis = 1, it becomes the ith column). There are three exceptions to this: when
i = len(indices)  1
(so for the last index),indices[i+1] = a.shape[axis]
.  if
indices[i] >= indices[i + 1]
, the ith generalized “row” is simplya[indices[i]]
.  if
indices[i] >= len(a)
orindices[i] < 0
, an error is raised.
The shape of the output depends on the size of
indices
, and may be larger than a (this happens iflen(indices) > a.shape[axis]
).Parameters:  a : array_like
The array to act on.
 indices : array_like
Paired indices, comma separated (not colon), specifying slices to reduce.
 axis : int, optional
The axis along which to apply the reduceat.
 dtype : datatype code, optional
The type used to represent the intermediate results. Defaults to the data type of the output array if this is provided, or the data type 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.
Returns:  r : ndarray
The reduced values. If out was supplied, r is a reference to out.
Notes
A descriptive example:
If a is 1D, the function ufunc.accumulate(a) is the same as
ufunc.reduceat(a, indices)[::2]
whereindices
isrange(len(array)  1)
with a zero placed in every other element:indices = zeros(2 * len(a)  1)
,indices[1::2] = range(1, len(a))
.Don’t be fooled by this attribute’s name: reduceat(a) is not necessarily smaller than a.
Examples
To take the running sum of four successive values:
>>> np.add.reduceat(np.arange(8),[0,4, 1,5, 2,6, 3,7])[::2] array([ 6, 10, 14, 18])
A 2D example:
>>> x = np.linspace(0, 15, 16).reshape(4,4) >>> x array([[ 0., 1., 2., 3.], [ 4., 5., 6., 7.], [ 8., 9., 10., 11.], [ 12., 13., 14., 15.]])
# reduce such that the result has the following five rows: # [row1 + row2 + row3] # [row4] # [row2] # [row3] # [row1 + row2 + row3 + row4]
>>> np.add.reduceat(x, [0, 3, 1, 2, 0]) array([[ 12., 15., 18., 21.], [ 12., 13., 14., 15.], [ 4., 5., 6., 7.], [ 8., 9., 10., 11.], [ 24., 28., 32., 36.]])
# reduce such that result has the following two columns: # [col1 * col2 * col3, col4]
>>> np.multiply.reduceat(x, [0, 3], 1) array([[ 0., 3.], [ 120., 7.], [ 720., 11.], [ 2184., 15.]])
 when