	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.

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:

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

d1: DENSITY SPECIESthis keyword is used for colvars such as coordination number. 
=1-7 The DENSITY action with label d1
mat: CONTACT_MATRIX ATOMSThe list of atoms for which you would like to calculate the contact matrix. 
=d1 SWITCHThis keyword is used if you want to employ an alternative to the continuous switching
function defined above. 
={RATIONAL R_0=0.1}  The CONTACT_MATRIX action with label mat
ss: SPRINT MATRIXcompulsory keyword 
the action that calculates the adjacency matrix vessel we would like to analyze 
=mat The SPRINT action with label ss calculates the following quantities:

 Quantity    Description  
ss.coord-0 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 0th of these quantities
ss.coord-1 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 1th of these quantities
ss.coord-2 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 2th of these quantities
ss.coord-3 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 3th of these quantities
ss.coord-4 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 4th of these quantities
ss.coord-5 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 5th of these quantities
ss.coord-6 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 6th of these quantities


PRINT ARGthe input for this action is the scalar output from one or more other actions. 
=ss.* FILEthe name of the file on which to output these quantities 
=colvar The PRINT action with label

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

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

c: DENSITY SPECIESthis keyword is used for colvars such as coordination number. 
=1-7 The DENSITY action with label c
h: DENSITY SPECIESthis keyword is used for colvars such as coordination number. 
=8-14 The DENSITY action with label h
mat: CONTACT_MATRIX ...
   ATOMSThe list of atoms for which you would like to calculate the contact matrix. 
=c,h 
   SWITCH11This keyword is used if you want to employ an alternative to the continuous switching
function defined above. ={RATIONAL R_0=2.6 NN=6 MM=12}  
   SWITCH12This keyword is used if you want to employ an alternative to the continuous switching
function defined above. ={RATIONAL R_0=2.2 NN=6 MM=12}  
   SWITCH22This keyword is used if you want to employ an alternative to the continuous switching
function defined above. ={RATIONAL R_0=2.2 NN=6 MM=12}  
   
...The CONTACT_MATRIX action with label mat
ss: SPRINT MATRIXcompulsory keyword 
the action that calculates the adjacency matrix vessel we would like to analyze 
=mat The SPRINT action with label ss calculates the following quantities:

 Quantity    Description  
ss.coord-0 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 0th of these quantities
ss.coord-1 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 1th of these quantities
ss.coord-2 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 2th of these quantities
ss.coord-3 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 3th of these quantities
ss.coord-4 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 4th of these quantities
ss.coord-5 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 5th of these quantities
ss.coord-6 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 6th of these quantities
ss.coord-7 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 7th of these quantities
ss.coord-8 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 8th of these quantities
ss.coord-9 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 9th of these quantities
ss.coord-10 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 10th of these quantities
ss.coord-11 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 11th of these quantities
ss.coord-12 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 12th of these quantities
ss.coord-13 all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on  This is the 13th of these quantities


PRINT ARGthe input for this action is the scalar output from one or more other actions. 
=ss.* FILEthe name of the file on which to output these quantities 
=colvar The PRINT action with label

Glossary of keywords and components

Description of components

By default this Action calculates the following quantities. 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
coord	all \(n\) sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled 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 referred to elsewhere in the input file by using the label.vmean
vsum	VSUM	the norm of sum of vectors. The output component can be referred 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 highest of the quantities 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 quantities 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 referred 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 calculates the adjacency matrix vessel we would like to analyze

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 use MPI
LOWMEM	( default=off ) lower the memory requirements
TIMINGS	( default=off ) output information on the timings of the various parts of the calculation

Quantity	Description
ss.coord-0	all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on This is the 0th of these quantities
ss.coord-1	all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on This is the 1th of these quantities
ss.coord-2	all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on This is the 2th of these quantities
ss.coord-3	all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on This is the 3th of these quantities
ss.coord-4	all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on This is the 4th of these quantities
ss.coord-5	all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on This is the 5th of these quantities
ss.coord-6	all \f$n\f$ sprint coordinates are calculated and then stored in increasing order. the smallest sprint coordinate will be labeled label.coord-1, the second smallest will be labelled label.coord-1 and so on This is the 6th of these quantities