numpy.outer

numpy.outer(a, b, out=None)

Compute the outer product of two vectors.

Given two vectors, a = [a0, a1, ..., aM] and b = [b0, b1, ..., bN], the outer product [R107107] 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.

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 N dimensions and other operations. np.multiply.outer(a.ravel(), b.ravel()) is the equivalent.

References

[R107107]

(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)