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 computes ufunc.reduce(a[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 two 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 i-th generalized “row” is simply a[indices[i]].

The shape of the output depends on the size of indices, and may be larger than a (this happens if len(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 : data-type 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, optional

A location into which the result is stored. If not provided a freshly-allocated array is returned.

Returns:

r : ndarray

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

Notes

A descriptive example:

If a is 1-D, the function ufunc.accumulate(a) is the same as ufunc.reduceat(a, indices)[::2] where indices is range(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 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.]])