# numpy.ma.outerproduct¶

`numpy.ma.``outerproduct`(a, b)[source]

Compute the outer product of two vectors.

Given two vectors, `a = [a0, a1, ..., aM]` and `b = [b0, b1, ..., bN]`, the outer product [R56] is:

```[[a0*b0  a0*b1 ... a0*bN ]
[a1*b0    .
[ ...          .
[aM*b0            aM*bN ]]
```
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. out : (M, N) ndarray `out[i, j] = a[i] * b[j]`

`inner`

`einsum`
`einsum('i,j->ij', a.ravel(), b.ravel())` is the equivalent.
`ufunc.outer`
A generalization to N dimensions and other operations. `np.multiply.outer(a.ravel(), b.ravel())` is the equivalent.

Notes

Masked values are replaced by 0.

References

 [R56] (1, 2) : 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)
```

numpy.ma.outer

numpy.ma.trace