Low Computational Performance ``kalman_time_dependent``

[nilsnevertree]

The Kalman algorithms using time independent Model M are very slow! It should be clear that the performance in of order $O(n) \cdot O(\text{classic})$ with n being the timesteps, and classic refering to the order of computation time of the classic Kalman algorithms.

[nilsnevertree]

We could reduce computation time by only using a certain slice of the arrays to perform the sklearn.LinearRegression() on. Thus setting an $\epsilon$ for which the kernel is set to 0 and no regression should be performed.

[nilsnevertree]

And we could try to vectorize the local linear regression problem, as the calculations are indepent of each other.

[nilsnevertree]

For x haveing 1000 elements along the time axis we get this:

kalman.Kalman_SEM()
100%|██████████| 10/10 [00:01<00:00,  5.27it/s]

kalman_time_dependent.Kalman_SEM_time_dependent()
100%|██████████| 10/10 [00:08<00:00,  1.12it/s]

[nilsnevertree]

It might help to use np.einsum for the local linear interpolation to speed things up.