jax.numpy.outer

jax.numpy.outer(a, b, out=None)[source]

Compute the outer product of two vectors.

LAX-backend implementation of outer(). Original docstring below.

Given two vectors, a = [a0, a1, ..., aM] and b = [b0, b1, ..., bN], the outer product 1 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

Returns

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

Return type

(M, N) ndarray

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)