xorbits.numpy.outer#

xorbits.numpy.outer(a, b, out=None)#

Compute the outer product of two vectors.

Given two vectors a and b of length M and N, repsectively, 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(numpy).

Returns

outout[i, j] = a[i] * b[j]

Return type

(M, N) ndarray

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.

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:

>>> 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)

Warning

This method has not been implemented yet. Xorbits will try to execute it with numpy.

This docstring was copied from numpy.