Calculate Difference Between All Combinations Of Entries In A Vector

I have a numpy 1D array of z values, and I want to calculate the difference between all combinations of the entries, with the output as a square matrix. I know how to calculate th

Solution 1:

Simple one line solution using numpy array broadcasting.

import numpy as np

z = np.array([1, 5, 8])
# Simple one line solution
z - z.reshape(-1,1)

Output:

array([[ 0,  4,  7],
       [-4,  0,  3],
       [-7, -3,  0]])

Solution 2:

In [29]: z = np.array([1, 5, 8])                                                                                                                                                                     

In [30]: -np.subtract.outer(z, z)                                                                                                                                                                    
Out[30]: 
array([[ 0,  4,  7],
       [-4,  0,  3],
       [-7, -3,  0]])

(Drop the minus sign if you don't care about the sign convention.)

Solution 3:

I've worked out I can get the answer I want with a double iterator, although I'm not sure it is the most efficient for very large arrays

np.array([j-i for i in z for j in z]).reshape(len(z),len(z))

output:

array([[ 0,  4,  7],
   [-4,  0,  3],
   [-7, -3,  0]])

EDIT: so indeed the other two solutions are about 50 times faster:

python3 -m timeit -s "import numpy as np" -s "z=np.random.uniform(size=5000)""z-z.reshape(-1,1)"2 loops, best of 5: 119 msec per loop

python3 -m timeit -s "import numpy as np" -s "z=np.random.uniform(size=5000)""np.subtract.outer(z, z)"2 loops, best of 5: 118 msec per loop

python3 -m timeit -s "import numpy as np" -s "z=np.random.uniform(size=5000)""np.array([j-i for i in z for j in z]).reshape(len(z),len(z))"1loop, best of 5: 5.18 sec per loop