Waleed Esmail :
I have four numpy arrays, and example given below:
a1=np.array([[-24.4925, 295.77 ],
[-24.4925, 295.77 ],
[-14.3925, 295.77 ],
[-16.4125, 295.77 ],
[-43.6825, 295.77 ],
[-22.4725, 295.77 ]])
a2=np.array([[-26.0075, 309.39 ],
[-24.9975, 309.39 ],
[-14.8975, 309.39 ],
[-17.9275, 309.39 ],
[-46.2075, 309.39 ],
[-23.9875, 309.39 ]])
a3=np.array([[-25.5025, 310.265 ],
[-25.5025, 310.265 ],
[-15.4025, 310.265 ],
[-17.4225, 310.265 ],
[-45.7025, 310.265 ],
[-24.4925, 310.265 ]])
a4=np.array([[-27.0175, 326.895 ],
[-27.0175, 326.895 ],
[-15.9075, 326.895 ],
[-18.9375, 326.895 ],
[-48.2275, 326.895 ],
[-24.9975, 326.895 ]])
I want to make all possible combinations between arrays and at the same time concatenate, for example:
array[-24.4925, 295.77, -26.0075, 309.39, -25.5025, 310.265, -27.0175, 326.895]
and
array[-24.4925, 295.77, -26.0075, 309.39, -25.5025, 310.265, -27.0175, 326.895]
that is [a1[0],a2[0],a3[0],a4[0]], [a1[0],a2[0],a3[0],a4[1]] and so on
what is the fastest method to it other than to loop over the four arrays?!
hilberts_drinking_problem :
Here is a numpy solution, based on the Cartesian product implementation from here.
arr = np.stack([a1, a2, a3, a4])
print(arr.shape) # (4, 6, 2)
n, m, k = arr.shape
# from https://stackoverflow.com/questions/11144513/cartesian-product-of-x-and-y-array-points-into-single-array-of-2d-points
def cartesian_product(*arrays):
la = len(arrays)
dtype = np.result_type(*arrays)
arr = np.empty([len(a) for a in arrays] + [la], dtype=dtype)
for i, a in enumerate(np.ix_(*arrays)):
arr[...,i] = a
return arr.reshape(-1, la)
inds = cartesian_product(*([np.arange(m)] * n))
res = np.take_along_axis(arr, inds.T[...,None], 1).swapaxes(0,1).reshape(-1, n*k)
print(res[0])
# [-24.4925 295.77 -26.0075 309.39 -25.5025 310.265 -27.0175 326.895 ]
In this example, the inds array looks as follows:
print(inds[:10])
# [[0 0 0 0]
# [0 0 0 1]
# [0 0 0 2]
# [0 0 0 3]
# [0 0 0 4]
# [0 0 0 5]
# [0 0 1 0]
# [0 0 1 1]
# [0 0 1 2]
# [0 0 1 3]]
We can then use np.take_along_axis to select appropriate elements for each combination.
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