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# numpy.prod

numpy.prod(a, axis=None, dtype=None, out=None, keepdims=<no value>, initial=<no value>, where=<no value>)

  Return the product of array elements over a given axis.

  Parameters:
    a array_like

      Input data.

    axis None or int or tuple of ints, optional

      Axis or axes along which a product is performed. The default, axis=None, will calculate the product of all the elements in the input array. If axis is negative it counts from the last to the first axis.

      If axis is a tuple of ints, a product is performed on all of the axes specified in the tuple instead of a single axis or all the axes as before.

    dtype dtype, optional

      The type of the returned array, as well as of the accumulator in which the elements are multiplied. The dtype of a is used by default unless a has an integer dtype of less precision than the default platform integer. In that case, if a is signed then the platform integer is used while if a is unsigned then an unsigned integer of the same precision as the platform integer is used.

    out ndarray, optional

      Alternative output array in which to place the result. It must have the same shape as the expected output, but the type of the output values will be cast if necessary.

    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 input array.

      If the default value is passed, then keepdims will not be passed through to the `prod` method of sub-classes of `ndarray`, however any non-default value will be. If the sub-class’ method does not implement keepdims any exceptions will be raised.

    initial scalar, optional

      The starting value for this product. See `reduce` for details.

    where array_like of bool, optional

      Elements to include in the product. See `reduce` for details.

  Returns:
    product_along_axis ndarray, see `dtype` parameter above.

      An array shaped as a but with the specified axis removed. Returns a reference to out if specified.

  See also

  `ndarray.prod`

    equivalent method

  Output type determination

  Notes

  Arithmetic is modular when using integer types, and no error is raised on overflow. That means that, on a 32-bit platform:

      >>> x = np.array([536870910, 536870910, 536870910, 536870910])
      >>> np.prod(x)
      16 # may vary

  The product of an empty array is the neutral element 1:

      >>> np.prod([])
      1.0

  Examples

  By default, calculate the product of all elements:

      >>> import numpy as np
      >>> np.prod([1.,2.])
      2.0

  Even when the input array is two-dimensional:

      >>> a = np.array([[1., 2.], [3., 4.]])
      >>> np.prod(a)
      24.0

  But we can also specify the axis over which to multiply:

      >>> np.prod(a, axis=1)
      array([  2.,  12.])
      >>> np.prod(a, axis=0)
      array([3., 8.])

  Or select specific elements to include:

      >>> np.prod([1., np.nan, 3.], where=[True, False, True])
      3.0

  If the type of x is unsigned, then the output type is the unsigned platform integer:

      >>> x = np.array([1, 2, 3], dtype=np.uint8)
      >>> np.prod(x).dtype == np.uint
      True

  If x is of a signed integer type, then the output type is the default platform integer:

      >>> x = np.array([1, 2, 3], dtype=np.int8)
      >>> np.prod(x).dtype == int
      True

  You can also start the product with a value other than one:

      >>> np.prod([1, 2], initial=5)
      10