# 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
    array 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, 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
    r ndarray

      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

  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.]])

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