Tprime evaluation and Solve TICA problem with not-symmetric Correlation Matrix

[nicolopedrani]

Description

• [ ] definition of tprime_evaluation function outside create_time_lagged_dataset function.
• [ ] Now it's possible to pass a tprime argument (optional) to create_time_lagged_dataset. If not passed then the rescaled time is computed from the unbias time and logweights
• [ ] Attribute symmetrize added to TICA object. Default value set to True, and enforce the symmetrization of Correlation matrices. If set to False the Compute_TICA function solve the TICA problem without symmetrizing C_tau

Todos

• check what happens if the correlation matrices are not symmetric

Questions

• [ ] The dataset is composed by the correlated couples ( x_i(t) , x_i(t+lag) ). When the data is divided between training set and validation set (RandomSplit) what does it happen to the time ordering of this set? is the correlation matrix computed properly? the time ordering is not important (the correlation matrix is simply a weighted average), but dividing the whole dataset into two different datasets may lead to different estimation of both C_tau and C_0, compared to the estimation obtained by using the whole dataset.
• [ ] what does it happend if the eigenvales and eigenfunctions are complex ?

Status

• [ ] Ready to go

[codecov-commenter]

Codecov Report

Merging #13 (a636ae4) into main (6567fb0) will decrease coverage by 0.97%. The diff coverage is 56.00%.

[luigibonati]

@nicolopedrani why did you add a new function correlation_matrices?

[nicolopedrani]

@nicolopedrani why did you add a new function correlation_matrices?

I will remove that. It was a test, to check if it is different to evaluate the covariances using all data. Tomorrow I will remove that "new" implentation Don't work until late

[luigibonati]

ok, when you remove it i will merge this PR. for experimental features it is better to work on different branches

Il giorno mer 8 giu 2022 alle ore 23:36 nicolò @.***> ha scritto:

@nicolopedrani https://github.com/nicolopedrani why did you add a new function correlation_matrices?

I will remove that. It was a test, to check if it is different to evaluate the covariances using all data. Tomorrow I will remove that "new" implentation Don't work until late

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