numpy.ufunc.outer¶

method

ufunc.outer(A, B, /, **kwargs)¶

Apply the ufunc op to all pairs (a, b) with a in A and b in B.

Let M = A.ndim, N = B.ndim. Then the result, C, of op.outer(A, B) is an array of dimension M + N such that:

\[C[i_0, ..., i_{M-1}, j_0, ..., j_{N-1}] = op(A[i_0, ..., i_{M-1}], B[j_0, ..., j_{N-1}])\]

For A and B one-dimensional, this is equivalent to:

r = empty(len(A),len(B))
for i in range(len(A)):
    for j in range(len(B)):
        r[i,j] = op(A[i], B[j])  # op = ufunc in question

Parameters

Aarray_like: First array
Barray_like: Second array
kwargsany: Arguments to pass on to the ufunc. Typically dtype or out. See ufunc for a comprehensive overview of all available arguments.

Returns

rndarray: Output array

See also

numpy.outer: A less powerful version of np.multiply.outer that ravels all inputs to 1D. This exists primarily for compatibility with old code.
tensordot: np.tensordot(a, b, axes=((), ())) and np.multiply.outer(a, b) behave same for all dimensions of a and b.

Examples

>>> np.multiply.outer([1, 2, 3], [4, 5, 6])
array([[ 4,  5,  6],
       [ 8, 10, 12],
       [12, 15, 18]])

A multi-dimensional example:

>>> A = np.array([[1, 2, 3], [4, 5, 6]])
>>> A.shape
(2, 3)
>>> B = np.array([[1, 2, 3, 4]])
>>> B.shape
(1, 4)
>>> C = np.multiply.outer(A, B)
>>> C.shape; C
(2, 3, 1, 4)
array([[[[ 1,  2,  3,  4]],
        [[ 2,  4,  6,  8]],
        [[ 3,  6,  9, 12]]],
       [[[ 4,  8, 12, 16]],
        [[ 5, 10, 15, 20]],
        [[ 6, 12, 18, 24]]]])

numpy.ufunc.at

numpy.ufunc.reduce