ma.outer(a, b)
Compute the outer product of two vectors.
Given two vectors a and b of length M and N, respectively, the outer product
is:
[[a_0*b_0a_0*b_1...a_0*b_{N-1}][a_1*b_0.[....[a_{M-1}*b_0a_{M-1}*b_{N-1}]]Parameters:a(M,) array_likeFirst input vector. Input is flattened if not already 1-dimensional.
b(N,) array_likeSecond input vector. Input is flattened if not already 1-dimensional.
out(M, N) ndarray, optionalA location where the result is stored
Returns:out(M, N) ndarrayout[i,j]=a[i]*b[j]
See also
einsum('i,j->ij',a.ravel(),b.ravel()) is the equivalent.
A generalization to dimensions other than 1D and other operations. np.multiply.outer(a.ravel(),b.ravel()) is the equivalent.
An Array API compatible variation of np.outer, which accepts 1-dimensional inputs only.
np.tensordot(a.ravel(),b.ravel(),axes=((),())) is the equivalent.
Notes
Masked values are replaced by 0.
References
[
]
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:
>>> importnumpyasnp>>> rl=np.outer(np.ones((5,)),np.linspace(-2,2,5))>>> rlarray([[-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,)))>>> imarray([[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>>> gridarray([[-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=np.object_)>>> np.outer(x,[1,2,3])array([['a', 'aa', 'aaa'], ['b', 'bb', 'bbb'], ['c', 'cc', 'ccc']], dtype=object)