Covariance calculation — mdaencore.covariance

The module contains functions to estimate the covariance matrix of an ensemble of structures.

mdaencore.covariance.covariance_matrix(ensemble, select='name CA', estimator=<function shrinkage_covariance_estimator>, weights='mass', reference=None)[source]

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 – Covariance matrix

Return type:

numpy.array

mdaencore.covariance.ml_covariance_estimator(coordinates, reference_coordinates=None)[source]

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 – Estimate of covariance matrix

Return type:

numpy.array

mdaencore.covariance.shrinkage_covariance_estimator(coordinates, reference_coordinates=None, shrinkage_parameter=None)[source]

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 – Covariance matrix

Return type:

nump.array