# 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:

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.

Returns
rndarray

Output array

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]]]])
```

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numpy.ufunc.at