I have a 3D tensor T of size (nrows, ncols, ncols), which I would like to multiply with a vector x of size nrows.
However, T will be a huge sparse tensor with 6×6 nonzero entries in each row;
thus, it would be useful to store T in a sparse format.
The most convenient way would be to define a Tsparse tensor of size (nrows, 6, 6) and a “pointer” matrix p of size (nrows, 6) which stores the indices of the nonzero entries for each row.

In this case, how can Tsparse and x multiplied in a Python code? If there were a direct way using NumPy or SciPy, I would highly prefer that option.

Anyway, here is my MWE, which needs to be rewritten based on what was stated above:

import numpy as np

nrows = 100
ncols = 20
p = np.zeros((nrows, 6), dtype=int)

for i in range(nrows):
    p[i, :] = np.random.choice(np.arange(ncols), 6, replace=False)

T = np.zeros((nrows, ncols, ncols))
Tsparse = np.zeros((nrows, 6, 6))
for i in range(nrows):
    for j in range(6):
        for k in range(6):
            entry = np.random.rand()
            T[i, p[i, j], p[i, k]] = entry
            Tsparse[i, j, k] = entry
            
x = np.array(np.random.rand(nrows))

res = np.tensordot(T, x, axes=([0], [0]))

print(res)