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Covariance calculation --- :mod:`encore.covariance`
=====================================================================
The module contains functions to estimate the covariance matrix of
an ensemble of structures.
:Author: Matteo Tiberti, Wouter Boomsma, Tone Bengtsen
.. versionadded:: 0.16.0
.. deprecated:: 2.8.0
This module is deprecated in favour of the
MDAKit `mdaencore `_ and will be removed
in MDAnalysis 3.0.0.
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Standard maximum likelihood estimator of the covariance matrix.
Parameters
----------
coordinates : numpy.array
Flattened array of coordiantes
reference_coordinates : numpy.array
Optional reference to use instead of mean
Returns
-------
cov_mat : numpy.array
Estimate of covariance matrix
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Shrinkage estimator of the covariance matrix using the method described in
Improved Estimation of the Covariance Matrix of Stock Returns With an
Application to Portfolio Selection. Ledoit, O.; Wolf, M., Journal of
Empirical Finance, 10, 5, 2003
This implementation is based on the matlab code made available by Olivier
Ledoit on his website:
http://www.ledoit.net/ole2_abstract.htm
Parameters
----------
coordinates : numpy.array
Flattened array of coordinates
reference_coordinates: numpy.array
Optional reference to use instead of mean
shrinkage_parameter: None or float
Optional shrinkage parameter
Returns
--------
cov_mat : nump.array
Covariance matrix
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Calculates (optionally mass weighted) covariance matrix
Parameters
----------
ensemble : Universe object
The structural ensemble
select : str (optional)
Atom selection string in the MDAnalysis format.
estimator : function (optional)
Function that estimates the covariance matrix. It requires at least
a "coordinates" numpy array (of shape (N,M,3), where N is the number
of frames and M the number of atoms). See ml_covariance_estimator and
shrinkage_covariance_estimator for reference.
weights : str/array_like (optional)
specify weights. If ``'mass'`` then chose masses of ensemble atoms, if ``None`` chose uniform weights
reference : MDAnalysis.Universe object (optional)
Use the distances to a specific reference structure rather than the
distance to the mean.
Returns
-------
cov_mat : numpy.array
Covariance matrix
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