numpy.ufunc.reduceat#
method
- ufunc.reduceat(array, 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(array[indices[i]:indices[i+1]])
, which becomes the i-th generalized “row” parallel to axis in the final result (i.e., in a 2-D array, for example, if axis = 0, it becomes the i-th row, but if axis = 1, it becomes the i-th column). There are three exceptions to this:when
i = len(indices) - 1
(so for the last index),indices[i+1] = array.shape[axis]
.if
indices[i] >= indices[i + 1]
, the i-th generalized “row” is simplyarray[indices[i]]
.if
indices[i] >= len(array)
orindices[i] < 0
, an error is raised.
The shape of the output depends on the size of
indices
, and may be larger thanarray
(this happens iflen(indices) > array.shape[axis]
).- Parameters:
- arrayarray_like
The array to act on.
- indicesarray_like
Paired indices, comma separated (not colon), specifying slices to reduce.
- axisint, optional
The axis along which to apply the reduceat.
- dtypedata-type code, optional
The data type used to perform the operation. Defaults to that of
out
if given, and the data type ofarray
otherwise (though upcast to conserve precision for some cases, such asnumpy.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.Changed in version 1.13.0: Tuples are allowed for keyword argument.
- Returns:
- rndarray
The reduced values. If out was supplied, r is a reference to out.
Notes
A descriptive example:
If
array
is 1-D, the function ufunc.accumulate(array) is the same asufunc.reduceat(array, indices)[::2]
whereindices
isrange(len(array) - 1)
with a zero placed in every other element:indices = zeros(2 * len(array) - 1)
,indices[1::2] = range(1, len(array))
.Don’t be fooled by this attribute’s name: reduceat(array) is not necessarily smaller than
array
.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 2-D 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.]])