`numpy:outer`

source: /dev/numpy/build-install/usr/lib/python3.14/site-packages/numpy/_core/numeric.py:909

Signature

def outer(a, b, out = None)

Summary

Compute the outer product of two vectors.

Extended Summary

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

[[a_0*b_0  a_0*b_1 ... a_0*b_{N-1} ]
 [a_1*b_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]

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
im = np.outer(1j*np.linspace(2, -2, 5), np.ones((5,)))
im
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)

Aliases

numpy.outer