numpy.outer#

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

Compute the outer product of two vectors.

Given two vectorsa andb of lengthM andN, respectively,the outer product[1] 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_like

First input vector. Input is flattened ifnot already 1-dimensional.

b(N,) array_like

Second input vector. Input is flattened ifnot 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 ofnp.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, 3rded., 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=object)>>>np.outer(x,[1,2,3])array([['a', 'aa', 'aaa'],       ['b', 'bb', 'bbb'],       ['c', 'cc', 'ccc']], dtype=object)
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