Python n-dimensional array combinations

Suppose an arbitrary number of arrays of arbitrary length. I would like to construct the n-dimensional array of all the combinations from the values in the arrays. Or even better, a list of all the combinations.

However, I would also like the previous "diagonal" element along each combination, except when such an element does not exist, in which case the values which do not exist are set to say -inf.

Take for ex. the following simple 2-D case:

v1=[-2,2]
v2=[-3,3]

From which I would get all the combinations

[[-2,-3],  
 [-2,3],  
 [2,-3],  
 [2,3]]

Or in 2D array / matrix form

      -3     3
-2  -2,-3  -2,3
 2   2,-3   2,3

Now I would also like a new column with the previous "diagonal" elements (in this case there is only 1 real such case) for each element. By previous "diagonal" element I mean the element at index i-1, j-1, k-1, ..., n-1. On the margins we take all the previous values that are possible.

  1      2
-2,-3  -inf,-inf
-2, 3  -inf,-3
 2,-3  -2,-inf
 2, 3  -2,-3

Edit: here is the code for the 2D case, which is not much use for the general n-case.

import math

v1=[-3,-1,2,4]
v2=[-2,0,2]

tmp=[]
tmp2=[]
for i in range(0,len(v1)):
    for j in range(0,len(v2)):
        tmp.append([v1[i],v2[j]])
        if i==0 and j==0:
            tmp2.append([-math.inf,-math.inf])
        elif i==0:
            tmp2.append([-math.inf,v2[j-1]])
        elif j==0:
            tmp2.append([v1[i-1],-math.inf])
        else:
            tmp2.append([v1[i-1],v2[j-1]])

And so

tmp

[[-3, -2],
 [-3, 0],
 [-3, 2],
 [-1, -2],
 [-1, 0],
 [-1, 2],
 [2, -2],
 [2, 0],
 [2, 2],
 [4, -2],
 [4, 0],
 [4, 2]]

and

tmp2

[[-inf, -inf],
 [-inf, -2],
 [-inf, 0],
 [-3, -inf],
 [-3, -2],
 [-3, 0],
 [-1, -inf],
 [-1, -2],
 [-1, 0],
 [2, -inf],
 [2, -2],
 [2, 0]]

Take a look at itertools.product().

To get the "diagonals" you could take the product of the vectors indices instead of the vectors themselves. That way you can access the values of each combination aswell as the previous values of the combination.

Example:

import itertools

v1=[-2,2]
v2=[-3,3]
vectors = [v1, v2]

combs = list(itertools.product(*[range(len(v)) for v in vectors]))

print(combs)

[(0, 0), (0, 1), (1, 0), (1, 1)]

print([[vectors[vi][ci] for vi, ci in enumerate(comb)] for comb in combs])

[[-2, -3], [-2, 3], [2, -3], [2, 3]]

print([[(vectors[vi][ci-1] if ci > 0 else np.inf) for vi, ci in enumerate(comb)] for comb in combs])

[[inf, inf], [inf, -3], [-2, inf], [-2, -3]]