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

Calculate SPRINT topological variables from an adjacency matrix.

The SPRINT topological variables are calculated from the largest eigenvalue, \(\lambda\) of an \(n\times n\) adjacency matrix and its corresponding eigenvector, \(\mathbf{V}\), using:

\[ s_i = \sqrt{n} \lambda v_i \]

You can use different quantities to measure whether or not two given atoms/molecules are adjacent or not in the adjacency matrix. The simplest measure of adjacency is is whether two atoms/molecules are within some cutoff of each other. Further complexity can be added by insisting that two molecules are adjacent if they are within a certain distance of each other and if they have similar orientations.

Description of components

By default this Action calculates the following quantities. These quanties 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
coord	all \(n\) sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labelled label.coord-1, the second smallest will be labelleled label.coord-1 and so on

In addition the following quantities can be calculated by employing the keywords listed below

Quantity	Keyword	Description
gradient	GRADIENT	the gradient
vmean	VMEAN	the norm of the mean vector. The output component can be refererred to elsewhere in the input file by using the label.vmean
vsum	VSUM	the norm of sum of vectors. The output component can be refererred to elsewhere in the input file by using the label.vsum
spath	SPATH	the position on the path
gspath	GPATH	the position on the path calculated using trigonometry
gzpath	GPATH	the distance from the path calculated using trigonometry
zpath	ZPATH	the distance from the path
altmin	ALT_MIN	the minimum value. This is calculated using the formula described in the description of the keyword so as to make it continuous.
between	BETWEEN	the number/fraction of values within a certain range. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters.
highest	HIGHEST	the lowest of the quantitities calculated by this action
lessthan	LESS_THAN	the number of values less than a target value. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters.
lowest	LOWEST	the lowest of the quantitities calculated by this action
max	MAX	the maximum value. This is calculated using the formula described in the description of the keyword so as to make it continuous.
mean	MEAN	the mean value. The output component can be refererred to elsewhere in the input file by using the label.mean
min	MIN	the minimum value. This is calculated using the formula described in the description of the keyword so as to make it continuous.
moment	MOMENTS	the central moments of the distribution of values. The second moment would be referenced elsewhere in the input file using label.moment-2, the third as label.moment-3, etc.
morethan	MORE_THAN	the number of values more than a target value. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters.
sum	SUM	the sum of values

Compulsory keywords

MATRIX

the action that calcualtes the adjacency matrix vessel we would like to analyse

Options

NUMERICAL_DERIVATIVES	( default=off ) calculate the derivatives for these quantities numerically
NOPBC	( default=off ) ignore the periodic boundary conditions when calculating distances
SERIAL	( default=off ) do the calculation in serial. Do not parallelize
LOWMEM	( default=off ) lower the memory requirements
TIMINGS	( default=off ) output information on the timings of the various parts of the calculation

Examples

This example input calculates the 7 SPRINT coordinates for a 7 atom cluster of Lennard-Jones atoms and prints their values to a file. In this input the SPRINT coordinates are calculated in the manner described in ?? so two atoms are adjacent if they are within a cutoff:

DENSITY SPECIES=1-7 LABEL=d1
CONTACT_MATRIX ATOMS=d1 SWITCH={RATIONAL R_0=0.1} LABEL=mat
SPRINT MATRIX=mat LABEL=ss
PRINT ARG=ss.* FILE=colvar

This example input calculates the 14 SPRINT coordinates foa a molecule composed of 7 hydrogen and 7 carbon atoms. Once again two atoms are adjacent if they are within a cutoff:

DENSITY SPECIES=1-7 LABEL=c
DENSITY SPECIES=8-14 LABEL=h

CONTACT_MATRIX ...
  ATOMS=c,h
  SWITCH11={RATIONAL R_0=2.6 NN=6 MM=12}
  SWITCH12={RATIONAL R_0=2.2 NN=6 MM=12}
  SWITCH22={RATIONAL R_0=2.2 NN=6 MM=12}
  LABEL=mat
... CONTACT_MATRIX

SPRINT MATRIX=mat LABEL=ss

PRINT ARG=ss.* FILE=colvar