numpy vectorize a function to accepts vectors of different lengths and return the tensor result

Question

I want to vectorize a function f(a, b) so that, when I enter a and b as two vectors, the tensor of combinations is returned. Here is an illustrative example:

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Answer 1

You can chain with np.ix_:

>>> import functools
>>> 
>>> def tensorize(f):
...     fv = np.vectorize(f)
...     @functools.wraps(f)
...     def ft(*args):
...         return fv(*np.ix_(*map(np.ravel, args)))
...     return ft
... 
>>> tester = tensorize(tester)
>>> tester(np.arange(3), np.arange(2))
array([[0., 0.],
       [0., 1.],
       [0., 4.]])