Numpy quirk: Apply function to all pairs of two 1D arrays, to get one 2D array

Question

Let\'s say I have 2 one-dimensional (1D) numpy arrays, a and b, with lengths n1 and n2 respectively. I also have a functi

Answer 1

If F() works with broadcast arguments, definitely use that, as others describe.
An alternative is to use np.fromfunction (function_on_an_int_grid would be a better name.) The following just maps the int grid to your a-b grid, then into F():

import numpy as np

def func_allpairs( F, a, b ):
    """ -> array len(a) x len(b):
        [[ F( a0 b0 )  F( a0 b1 ) ... ]
         [ F( a1 b0 )  F( a1 b1 ) ... ]
         ...
        ]
    """
    def fab( i, j ):
        return F( a[i], b[j] )  # F scalar or vec, e.g. gradient

    return np.fromfunction( fab, (len(a), len(b)), dtype=int )  # -> fab( all pairs )


#...............................................................................
def F( x, y ):
    return x + 10*y

a = np.arange( 100 )
b = np.arange( 222 )
A = func_allpairs( F, a, b )
# %timeit: 1000 loops, best of 3: 241 µs per loop -- imac i5, np 1.9.3