# dask.array.outer¶

dask.array.outer(a, b)[source]

Compute the outer product of two vectors.

This docstring was copied from numpy.outer.

Some inconsistencies with the Dask version may exist.

Given two vectors a and b of length `M` and `N`, repsectively, the outer product [1] is:

```[[a_0*b_0  a_0*b_1 ... a_0*b_{N-1} ]
[a_1*b_0    .
[ ...          .
[a_{M-1}*b_0            a_{M-1}*b_{N-1} ]]
```
Parameters
a(M,) array_like

First input vector. Input is flattened if not already 1-dimensional.

b(N,) array_like

Second input vector. Input is flattened if not already 1-dimensional.

out(M, N) ndarray, optional

A location where the result is stored

New in version 1.9.0.

Returns
out(M, N) ndarray

`out[i, j] = a[i] * b[j]`

See also

`inner`
`einsum`

`einsum('i,j->ij', a.ravel(), b.ravel())` is the equivalent.

`ufunc.outer`

A generalization to dimensions other than 1D and other operations. `np.multiply.outer(a.ravel(), b.ravel())` is the equivalent.

`tensordot`

`np.tensordot(a.ravel(), b.ravel(), axes=((), ()))` is the equivalent.

References

1

G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., Baltimore, MD, Johns Hopkins University Press, 1996, pg. 8.

Examples

Make a (very coarse) grid for computing a Mandelbrot set:

```>>> rl = np.outer(np.ones((5,)), np.linspace(-2, 2, 5))
>>> rl
array([[-2., -1.,  0.,  1.,  2.],
[-2., -1.,  0.,  1.,  2.],
[-2., -1.,  0.,  1.,  2.],
[-2., -1.,  0.,  1.,  2.],
[-2., -1.,  0.,  1.,  2.]])
>>> im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))
>>> im
array([[0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j, 0.+2.j],
[0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j, 0.+1.j],
[0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],
[0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j, 0.-1.j],
[0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j, 0.-2.j]])
>>> grid = rl + im
>>> grid
array([[-2.+2.j, -1.+2.j,  0.+2.j,  1.+2.j,  2.+2.j],
[-2.+1.j, -1.+1.j,  0.+1.j,  1.+1.j,  2.+1.j],
[-2.+0.j, -1.+0.j,  0.+0.j,  1.+0.j,  2.+0.j],
[-2.-1.j, -1.-1.j,  0.-1.j,  1.-1.j,  2.-1.j],
[-2.-2.j, -1.-2.j,  0.-2.j,  1.-2.j,  2.-2.j]])
```

An example using a “vector” of letters:

```>>> x = np.array(['a', 'b', 'c'], dtype=object)
>>> np.outer(x, [1, 2, 3])
array([['a', 'aa', 'aaa'],
['b', 'bb', 'bbb'],
['c', 'cc', 'ccc']], dtype=object)
```