# numpy.ufunc.reduce

method

ufunc.reduce(array, axis=0, dtype=None, out=None, keepdims=False, initial=<no value>, where=True)

  Reduces `array`’s dimension by one, by applying ufunc along one axis.

  Let \(array.shape = (N_0, ..., N_i, ..., N_{M-1})\). Then \(ufunc.reduce(array, axis=i)[k_0, ..,k_{i-1}, k_{i+1}, .., k_{M-1}]\) = the result of iterating j over \(range(N_i)\), cumulatively applying ufunc to each \(array[k_0, ..,k_{i-1}, j, k_{i+1}, .., k_{M-1}]\). For a one-dimensional array, reduce produces results equivalent to:

      r = op.identity # op = ufunc
      for i in range(len(A)):
        r = op(r, A[i])
      return r

  For example, add.reduce() is equivalent to sum().

  Parameters
    array array_like

      The array to act on.

    axis None or int or tuple of ints, optional

      Axis or axes along which a reduction is performed. The default (axis = 0) is perform a reduction over the first dimension of the input array. axis may be negative, in which case it counts from the last to the first axis.

      New in version 1.7.0.

      If this is None, a reduction is performed over all the axes. If this is a tuple of ints, a reduction is performed on multiple axes, instead of a single axis or all the axes as before.

      For operations which are either not commutative or not associative, doing a reduction over multiple axes is not well-defined. The ufuncs do not currently raise an exception in this case, but will likely do so in the future.

    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.

    keepdims bool, optional

      If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original `array`.

      New in version 1.7.0.

    initial scalar, optional

      The value with which to start the reduction. If the ufunc has no identity or the dtype is object, this defaults to None - otherwise it defaults to ufunc.identity. If `None` is given, the first element of the reduction is used, and an error is thrown if the reduction is empty.

      New in version 1.15.0.

    where array_like of bool, optional

      A boolean array which is broadcasted to match the dimensions of `array`, and selects elements to include in the reduction. Note that for ufuncs like `minimum` that do not have an identity defined, one has to pass in also `initial`.

      New in version 1.17.0.

  Returns
    r ndarray

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

  Examples

      >>> np.multiply.reduce([2,3,5])
      30

  A multi-dimensional array example:

      >>> X = np.arange(8).reshape((2,2,2))
      >>> X
      array([[[0, 1],
              [2, 3]],
             [[4, 5],
              [6, 7]]])
      >>> np.add.reduce(X, 0)
      array([[ 4,  6],
             [ 8, 10]])
      >>> np.add.reduce(X) # confirm: default axis value is 0
      array([[ 4,  6],
             [ 8, 10]])
      >>> np.add.reduce(X, 1)
      array([[ 2,  4],
             [10, 12]])
      >>> np.add.reduce(X, 2)
      array([[ 1,  5],
             [ 9, 13]])

  You can use the `initial` keyword argument to initialize the reduction with a different value, and `where` to select specific elements to include:

      >>> np.add.reduce([10], initial=5)
      15
      >>> np.add.reduce(np.ones((2, 2, 2)), axis=(0, 2), initial=10)
      array([14., 14.])
      >>> a = np.array([10., np.nan, 10])
      >>> np.add.reduce(a, where=~np.isnan(a))
      20.0

  Allows reductions of empty arrays where they would normally fail, i.e. for ufuncs without an identity.

      >>> np.minimum.reduce([], initial=np.inf)
      inf
      >>> np.minimum.reduce([[1., 2.], [3., 4.]], initial=10., where=[True, False])
      array([ 1., 10.])
      >>> np.minimum.reduce([])
      Traceback (most recent call last):
          ...
      ValueError: zero-size array to reduction operation minimum which has no identity

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