SIZESHAPE_POSITION_MAHA_DIST

	This is part of the sizeshape module
	It is only available if you configure PLUMED with ./configure –enable-modules=sizeshape . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list.

Calculates Mahalanobis distance of a current configuration from a given reference configurational distribution in size-and-shape space.

The Mahalanobis distance is given as:

\[d(\mathbf{x}, \mathbf{\mu}, \mathbf{\Sigma}) = \sqrt{(\mathbf{x}-\mathbf{\mu})^T \mathbf{\Sigma}^{-1} (\mathbf{x}-\mathbf{\mu})} \]

Here \(\mathbf{x}\) is the configuration at time t, \(\mathbf{\mu}\) is the reference and \(\mathbf{\Sigma}^{-1}\) is the \(N \times N\) precision matrix.

Size-and-shape Gaussian Mixture Model (shapeGMM) [Heidi-shapeGMM-2022] is a probabilistic clustering technique that is used to perform structural clusteing on ensemble of molecular configurations and to obtain reference \((\mathbf{\mu})\) and precision \((\mathbf{\Sigma}^{-1})\) corresponding to each of the cluster centers. Please chcek out shapeGMMTorch-GitHub and shapeGMMTorch-PyPI for examples and informations on preforming shapeGMM clustering.

Examples

In the following example, a group is defined with atom indices of selected atoms and then Mahalanobis distance is calculated with respect to the given reference and precision. Each file is a space separated list of 3N floating point numbers.

Click on the labels of the actions for more information on what each action computes

UNITS LENGTHthe units of lengths. =A TIMEthe units of time. =ps ENERGYthe units of energy. =kcal/mol  You cannot view the components that are calculated by each action for this input file. Sorry 
ga_list: GROUP ATOMSthe numerical indexes for the set of atoms in the group. =18,20,22,31,33,35,44,46,48,57,59,61,70,72,74,83,85,87,96,98,100,109,111  You cannot view the components that are calculated by each action for this input file. Sorry 
#SETTINGS AUXFILE=regtest/sizeshape/rt-mahadist/global_avg.txt
#SETTINGS AUXFILE=regtest/sizeshape/rt-mahadist/global_precision.txt
d: SIZESHAPE_POSITION_MAHA_DIST REFERENCEcompulsory keyword 
Reference structure. =global_avg.txt PRECISIONcompulsory keyword 
Precision Matrix (inverse of covariance) =global_precision.txt GROUPThe group of atoms being used. =ga_list  You cannot view the components that are calculated by each action for this input file. Sorry 
PRINT ARGthe input for this action is the scalar output from one or more other actions. =d STRIDEcompulsory keyword ( default=1 )
the frequency with which the quantities of interest should be output =1 FILEthe name of the file on which to output these quantities =output FMTthe format that should be used to output real numbers =%8.8f  You cannot view the components that are calculated by each action for this input file. Sorry 

Glossary of keywords and components

Description of components

By default the value of the calculated quantity can be referenced elsewhere in the input file by using the label of the action. Alternatively this Action can be used to calculate the following quantities by employing the keywords listed below. These quantities can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the quantity required from the list below.

Quantity	Description
.#!value	the Mahalanobis distance between the instantaneous configuration and a given reference distribution in size-and-shape space

The atoms involved can be specified using

GROUP

The group of atoms being used. For more information on how to specify lists of atoms see Groups and Virtual Atoms

Compulsory keywords

PRECISION	Precision Matrix (inverse of covariance)
REFERENCE	Reference structure.

Options

NUMERICAL_DERIVATIVES	( default=off ) calculate the derivatives for these quantities numerically
NOPBC	( default=off ) ignore the periodic boundary conditions when calculating distances
SQUARED	( default=off ) Returns the square of distance.