numpy.outer — NumPy v2.2 Manual (original) (raw)

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

Compute the outer product of two vectors.

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

[[a_0b_0 a_0b_1 ... a_0b_{N-1} ] [a_1b_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

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.

linalg.outer

An Array API compatible variation of np.outer, which accepts 1-dimensional inputs only.

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:

import numpy as np 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)