User guide: EM estimator for Generalized Langevin Equations¶
EM Estimator¶
The central piece of the package is the GLE_analysisEM.GLE_Estimator. All estimators in scikit-learn are derived
from this class. In more details, this base class enables to set and get
parameters of the estimator. It can be imported as:
>>> from GLE_analysisEM import GLE_Estimator
Once imported, lauching the estimation is as simple as
>>> estimator = GLE_Estimator(dim_x=dim_x, dim_h=dim_h, basis=basis)
>>> estimator.fit(X, idx_trajs=idx)
Several parameters are available. At least dim_x that give the dimension of the system under study and dim_h that give the number of hidden dimension to fit should be provided.
A functional basis for fitting of the mean force is also required and is explained below.
The trajectories data are provided to the GLE_analysisEM.fit function as X and idx under a format that is explained below.
Once fitted (that can be quite long), the estimated parameters can be obtained as a dictionary
>>> estimator.get_coefficients()
Functional basis¶
In GLE_analysisEM, the mean force term is fitted on a functional basis that should be provided to GLE_analysisEM.GLE_Estimator.
Functional basis are implemented in GLE_analysisEM.GLE_BasisTransform that could be imported and initialized as
>>> from GLE_analysisEM import GLE_BasisTransform
>>> basis = GLE_BasisTransform(basis_type="linear")
Several options are available for the type of basis, please refer to the documentation of GLE_analysisEM.GLE_BasisTransform. Some type required the basis to be fitted from the data a priori using
>>> basis = GLE_BasisTransform(basis_type="free_energy").fit(X)
Trajectory format¶
The trajectories should be pass as a single array of the shape (Ndatas x dim).
If multiple trajectories shoud be provided, all trajectories should be stacked together and another array that contain the indices to split the array should be provided (passed to numpy.split).
Helpers function that load trajectories from files (one file per trajectories) are provided in GLE_analysisEM.data_loaders.
Generation of new trajectories¶
Once the estimator is converged, it can be used to generate new trajectories with GLE_analysisEM.sample.