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:

aarray_like

Input data.

axisNone 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.

dtypedtype, 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.

outndarray, 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.

keepdimsbool, 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.

initialscalar, optional

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

wherearray_like of bool, optional

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

Returns:

product_along_axisndarray, 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