outer(a, b)

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

[[a0*b0  a0*b1 ... a0*bN ]
 [a1*b0    .
 [ ...          .
 [aM*b0            aM*bN ]]

Notes

Masked values are replaced by 0.

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

versionadded

Returns

out : (M, N) ndarray

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

Compute the outer product of two vectors.

See Also

einsum

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

inner

tensordot

np.tensordot(a.ravel(), b.ravel(), axes=((), ())) 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.

Examples

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

This example is valid syntax, but we were not able to check execution

>>> 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.]])

This example is valid syntax, but we were not able to check execution

>>> 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]])

This example is valid syntax, but we were not able to check execution

>>> 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:

This example is valid syntax, but we were not able to check execution

>>> 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)

See :

Local connectivity graph

Hover to see nodes names; edges to Self not shown, Caped at 50 nodes.

Using a canvas is more power efficient and can get hundred of nodes ; but does not allow hyperlinks; , arrows or text (beyond on hover)

SVG is more flexible but power hungry; and does not scale well to 50 + nodes.

All aboves nodes referred to, (or are referred from) current nodes; Edges from Self to other have been omitted (or all nodes would be connected to the central node "self" which is not useful). Nodes are colored by the library they belong to, and scaled with the number of references pointing them

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GitHub : /numpy/ma/core.py#7651
type: <class 'function'>
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