numpy.ma.outerproduct#
- ma.outerproduct(a, b)[source]#
Compute the outer product of two vectors.
Given two vectors a and b of length
M
andN
, 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
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 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.
Notes
Masked values are replaced by 0.
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:
>>> 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)