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 computes ufunc.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 simply array[indices[i]].
• if indices[i] >= len(array) or indices[i] < 0, an error is raised.

The shape of the output depends on the size of indices, and may be larger than array (this happens if len(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 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

Location into which the result is stored. If not provided or None, a freshly-allocated array is returned. For consistency with ufunc.__call__, if passed as a keyword argument, can be Ellipses (out=..., which has the same effect as None as an array is always returned), or a 1-element tuple.

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 as ufunc.reduceat(array, indices)[::2] where indices is range(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

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To take the running sum of four successive values:

>>> import numpy as np
>>> 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.]])

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