Shortcut: SPRINT

Module	sprint
Description	Usage
Calculate SPRINT topological variables from an adjacency matrix.

Details and examples

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, $V$ , using:

$s_i = \sqrt{n} \lambda v_i$

The example input below calculates the 7 SPRINT coordinates for a 7 atom cluster of Lennard-Jones atoms and prints their values to a file.

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

ss: SPRINTCalculate SPRINT topological variables from an adjacency matrix. This action is a shortcut. More details GROUPspecifies the list of atoms that should be assumed indistinguishable=1-7 SWITCHspecify the switching function to use between two sets of indistinguishable atoms={RATIONAL R_0=0.1}
# PLUMED interprets the command:
# ss: SPRINT GROUP=1-7 SWITCH={RATIONAL R_0=0.1}
# as follows (Click the red comment above to revert to the short version of the input):
The SPRINT action with label ss calculates the following quantities: Quantity    Description  
ss.coord the sprint coordinatesss_jmatThe CONTACT_MATRIX action with label ss_jmat calculates the following quantities: Quantity    Type    Description  
ss_jmat matrix a matrix containing the weights for the bonds between each pair of atoms: CONTACT_MATRIXAdjacency matrix in which two atoms are adjacent if they are within a certain cutoff. More details  GROUPspecifies the list of atoms that should be assumed indistinguishable=1-7 SWITCHthe input for the switching function that acts upon the distance between each pair of atoms. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=0.1}
ss_diagThe DIAGONALIZE action with label ss_diag calculates the following quantities: Quantity    Type    Description  
ss_diag.vals-1 scalar the eigevalues of the input matrix  This is the 1th of these quantities
ss_diag.vecs-1 vector the eigenvectors of the input matrix  This is the 1th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix More details ARGthe input matrix=ss_jmat VECTORS the eigenvalues and vectors that you would like to calculate=1
ss_spThe CUSTOM action with label ss_sp calculates the following quantities: Quantity    Type    Description  
ss_sp vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=ss_diag.vecs-1,ss_diag.vals-1 FUNCthe function you wish to evaluate=sqrt(7)*x*y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_selection1The SELECT_WITH_MASK action with label ss_selection1 calculates the following quantities: Quantity    Type    Description  
ss_selection1 vector a vector/matrix of values that is obtained using a mask to select elements of interest: SELECT_COMPONENTSCreate a new value to hold a subset of the components that are in a vector or matrix More details ARGthe value from which we are selecting components=ss_sp COMPONENTSthe components in the input value that you woul like to build a new vector from=1,2,3,4,5,6,7
ss1The SORT action with label ss1 calculates the following quantities: Quantity    Type    Description  
ss1.1 scalar the 1th largest element in the input vector
ss1.2 scalar the 2th largest element in the input vector
ss1.3 scalar the 3th largest element in the input vector
ss1.4 scalar the 4th largest element in the input vector
ss1.5 scalar the 5th largest element in the input vector
ss1.6 scalar the 6th largest element in the input vector
ss1.7 scalar the 7th largest element in the input vector: SORTThis function can be used to sort colvars according to their magnitudes. More details ARGthe values input to this function=ss_selection1
ss_coord-0The COMBINE action with label ss_coord-0 calculates the following quantities: Quantity    Type    Description  
ss_coord-0 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.1 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-1The COMBINE action with label ss_coord-1 calculates the following quantities: Quantity    Type    Description  
ss_coord-1 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-2The COMBINE action with label ss_coord-2 calculates the following quantities: Quantity    Type    Description  
ss_coord-2 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.3 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-3The COMBINE action with label ss_coord-3 calculates the following quantities: Quantity    Type    Description  
ss_coord-3 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.4 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-4The COMBINE action with label ss_coord-4 calculates the following quantities: Quantity    Type    Description  
ss_coord-4 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.5 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-5The COMBINE action with label ss_coord-5 calculates the following quantities: Quantity    Type    Description  
ss_coord-5 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.6 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-6The COMBINE action with label ss_coord-6 calculates the following quantities: Quantity    Type    Description  
ss_coord-6 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.7 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=ss.* FILEthe name of the file on which to output these quantities=colvar

This example input calculates the 14 SPRINT coordinates for a molecule composed of 7 hydrogen and 7 carbon atoms.

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

ss: SPRINTCalculate SPRINT topological variables from an adjacency matrix. This action is a shortcut. More details ...
  GROUP1specifies the list of atoms that should be assumed indistinguishable=1-7 GROUP2specifies the list of atoms that should be assumed indistinguishable=8-14
  SWITCH11specify the switching function to use between two sets of indistinguishable atoms={RATIONAL R_0=2.6 NN=6 MM=12}
  SWITCH12specify the switching function to use between two sets of indistinguishable atoms={RATIONAL R_0=2.2 NN=6 MM=12}
  SWITCH22specify the switching function to use between two sets of indistinguishable atoms={RATIONAL R_0=2.2 NN=6 MM=12}
...
# PLUMED interprets the command:
# ss: SPRINT ...
#   GROUP1=1-7 GROUP2=8-14
#   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}
# ...
# as follows (Click the red comment above to revert to the short version of the input):
The SPRINT action with label ss calculates the following quantities: Quantity    Description  
ss.coord the sprint coordinatesss_jmatThe CONCATENATE action with label ss_jmat calculates the following quantities: Quantity    Type    Description  
ss_jmat matrix the concatenated vector/matrix that was constructed from the input values: CONTACT_MATRIXAdjacency matrix in which two atoms are adjacent if they are within a certain cutoff. More details  GROUP1specifies the list of atoms that should be assumed indistinguishable=1-7 GROUP2specifies the list of atoms that should be assumed indistinguishable=8-14 SWITCH11the input for the switching function that acts upon the distance between each pair of atoms. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=2.6 NN=6 MM=12} SWITCH12the input for the switching function that acts upon the distance between each pair of atoms. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=2.2 NN=6 MM=12} SWITCH22the input for the switching function that acts upon the distance between each pair of atoms. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=2.2 NN=6 MM=12}
ss_diagThe DIAGONALIZE action with label ss_diag calculates the following quantities: Quantity    Type    Description  
ss_diag.vals-1 scalar the eigevalues of the input matrix  This is the 1th of these quantities
ss_diag.vecs-1 vector the eigenvectors of the input matrix  This is the 1th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix More details ARGthe input matrix=ss_jmat VECTORS the eigenvalues and vectors that you would like to calculate=1
ss_spThe CUSTOM action with label ss_sp calculates the following quantities: Quantity    Type    Description  
ss_sp vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=ss_diag.vecs-1,ss_diag.vals-1 FUNCthe function you wish to evaluate=sqrt(14)*x*y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_selection1The SELECT_WITH_MASK action with label ss_selection1 calculates the following quantities: Quantity    Type    Description  
ss_selection1 vector a vector/matrix of values that is obtained using a mask to select elements of interest: SELECT_COMPONENTSCreate a new value to hold a subset of the components that are in a vector or matrix More details ARGthe value from which we are selecting components=ss_sp COMPONENTSthe components in the input value that you woul like to build a new vector from=1,2,3,4,5,6,7
ss1The SORT action with label ss1 calculates the following quantities: Quantity    Type    Description  
ss1.1 scalar the 1th largest element in the input vector
ss1.2 scalar the 2th largest element in the input vector
ss1.3 scalar the 3th largest element in the input vector
ss1.4 scalar the 4th largest element in the input vector
ss1.5 scalar the 5th largest element in the input vector
ss1.6 scalar the 6th largest element in the input vector
ss1.7 scalar the 7th largest element in the input vector: SORTThis function can be used to sort colvars according to their magnitudes. More details ARGthe values input to this function=ss_selection1
ss_coord-0The COMBINE action with label ss_coord-0 calculates the following quantities: Quantity    Type    Description  
ss_coord-0 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.1 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-1The COMBINE action with label ss_coord-1 calculates the following quantities: Quantity    Type    Description  
ss_coord-1 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-2The COMBINE action with label ss_coord-2 calculates the following quantities: Quantity    Type    Description  
ss_coord-2 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.3 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-3The COMBINE action with label ss_coord-3 calculates the following quantities: Quantity    Type    Description  
ss_coord-3 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.4 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-4The COMBINE action with label ss_coord-4 calculates the following quantities: Quantity    Type    Description  
ss_coord-4 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.5 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-5The COMBINE action with label ss_coord-5 calculates the following quantities: Quantity    Type    Description  
ss_coord-5 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.6 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-6The COMBINE action with label ss_coord-6 calculates the following quantities: Quantity    Type    Description  
ss_coord-6 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss1.7 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_selection2The SELECT_WITH_MASK action with label ss_selection2 calculates the following quantities: Quantity    Type    Description  
ss_selection2 vector a vector/matrix of values that is obtained using a mask to select elements of interest: SELECT_COMPONENTSCreate a new value to hold a subset of the components that are in a vector or matrix More details ARGthe value from which we are selecting components=ss_sp COMPONENTSthe components in the input value that you woul like to build a new vector from=8,9,10,11,12,13,14
ss2The SORT action with label ss2 calculates the following quantities: Quantity    Type    Description  
ss2.1 scalar the 1th largest element in the input vector
ss2.2 scalar the 2th largest element in the input vector
ss2.3 scalar the 3th largest element in the input vector
ss2.4 scalar the 4th largest element in the input vector
ss2.5 scalar the 5th largest element in the input vector
ss2.6 scalar the 6th largest element in the input vector
ss2.7 scalar the 7th largest element in the input vector: SORTThis function can be used to sort colvars according to their magnitudes. More details ARGthe values input to this function=ss_selection2
ss_coord-7The COMBINE action with label ss_coord-7 calculates the following quantities: Quantity    Type    Description  
ss_coord-7 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss2.1 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-8The COMBINE action with label ss_coord-8 calculates the following quantities: Quantity    Type    Description  
ss_coord-8 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss2.2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-9The COMBINE action with label ss_coord-9 calculates the following quantities: Quantity    Type    Description  
ss_coord-9 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss2.3 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-10The COMBINE action with label ss_coord-10 calculates the following quantities: Quantity    Type    Description  
ss_coord-10 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss2.4 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-11The COMBINE action with label ss_coord-11 calculates the following quantities: Quantity    Type    Description  
ss_coord-11 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss2.5 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-12The COMBINE action with label ss_coord-12 calculates the following quantities: Quantity    Type    Description  
ss_coord-12 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss2.6 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ss_coord-13The COMBINE action with label ss_coord-13 calculates the following quantities: Quantity    Type    Description  
ss_coord-13 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=ss2.7 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- 
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=ss.* FILEthe name of the file on which to output these quantities=colvar

If you explore the inputs above you can see that when PLUMED reads them it creates a more complicated input file for calculating the SPRINT CVs. You can get a sense of how these CVs are calculated by looking at the expanded versions of the shortcuts in the inputs above. The insight into these methods that you can obtain by looking at these expanded input should hopefully give you ideas for developing new versions of these methods that use the same body of theory. For example, if you look at the inputs above you can see that one or more CONTACT_MATRIX actions are used to calculate sprint. These CONTACT_MATRIX determine whether atoms are adjacent or not. However, you can use different quantities to measure whether or not two given atoms/molecules are adjacent or not and compute a different type of adjacency matrix. For example you can say that two molecules are adjacent if they are within a certain distance of each other and if they have similar orientations or you can argue that two molecules are adjacent if there is a hydrogen bond between them.

In the example input below we measure adjacency between atoms using a BRIDGE_MATRIX and then compute the SPRINT CVs by diagonalizing this matrix.

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

bThe BRIDGE_MATRIX action with label b calculates the following quantities: Quantity    Type    Description  
b matrix a matrix containing the weights for the bonds between each pair of atoms: BRIDGE_MATRIXCalculate the number of atoms that bridge two parts of a structure This action has hidden defaults. More details GROUPthe atoms for which you would like to calculate the adjacency matrix=1-7 BRIDGING_ATOMSThe list of atoms that can form the bridge between the two interesting parts of the structure=8-100 SWITCHThe parameters of the two switching functions in the above formula. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=0.2}
b: BRIDGE_MATRIXCalculate the number of atoms that bridge two parts of a structure This action uses the defaults shown here. More details GROUPthe atoms for which you would like to calculate the adjacency matrix=1-7 BRIDGING_ATOMSThe list of atoms that can form the bridge between the two interesting parts of the structure=8-100 SWITCHThe parameters of the two switching functions in the above formula. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=0.2}  NL_CUTOFF The cutoff for the neighbor list=0.0 NL_STRIDE The frequency with which we are updating the atoms in the neighbor list=1
s: SPRINTCalculate SPRINT topological variables from an adjacency matrix. This action is a shortcut. More details MATRIXthe matrix that you would like to perform SPRINT on=b
# PLUMED interprets the command:
# s: SPRINT MATRIX=b
# as follows (Click the red comment above to revert to the short version of the input):
The SPRINT action with label s calculates the following quantities: Quantity    Description  
s.coord the sprint coordinatess_diagThe DIAGONALIZE action with label s_diag calculates the following quantities: Quantity    Type    Description  
s_diag.vals-1 scalar the eigevalues of the input matrix  This is the 1th of these quantities
s_diag.vecs-1 vector the eigenvectors of the input matrix  This is the 1th of these quantities: DIAGONALIZECalculate the eigenvalues and eigenvectors of a square matrix More details ARGthe input matrix=b VECTORS the eigenvalues and vectors that you would like to calculate=1
s_spThe CUSTOM action with label s_sp calculates the following quantities: Quantity    Type    Description  
s_sp vector the vector obtained by doing an element-wise application of an arbitrary function to the input vectors: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=s_diag.vecs-1,s_diag.vals-1 FUNCthe function you wish to evaluate=sqrt(7)*x*y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s_selection1The SELECT_WITH_MASK action with label s_selection1 calculates the following quantities: Quantity    Type    Description  
s_selection1 vector a vector/matrix of values that is obtained using a mask to select elements of interest: SELECT_COMPONENTSCreate a new value to hold a subset of the components that are in a vector or matrix More details ARGthe value from which we are selecting components=s_sp COMPONENTSthe components in the input value that you woul like to build a new vector from=1,2,3,4,5,6,7
s1The SORT action with label s1 calculates the following quantities: Quantity    Type    Description  
s1.1 scalar the 1th largest element in the input vector
s1.2 scalar the 2th largest element in the input vector
s1.3 scalar the 3th largest element in the input vector
s1.4 scalar the 4th largest element in the input vector
s1.5 scalar the 5th largest element in the input vector
s1.6 scalar the 6th largest element in the input vector
s1.7 scalar the 7th largest element in the input vector: SORTThis function can be used to sort colvars according to their magnitudes. More details ARGthe values input to this function=s_selection1
s_coord-0The COMBINE action with label s_coord-0 calculates the following quantities: Quantity    Type    Description  
s_coord-0 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=s1.1 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s_coord-1The COMBINE action with label s_coord-1 calculates the following quantities: Quantity    Type    Description  
s_coord-1 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=s1.2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s_coord-2The COMBINE action with label s_coord-2 calculates the following quantities: Quantity    Type    Description  
s_coord-2 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=s1.3 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s_coord-3The COMBINE action with label s_coord-3 calculates the following quantities: Quantity    Type    Description  
s_coord-3 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=s1.4 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s_coord-4The COMBINE action with label s_coord-4 calculates the following quantities: Quantity    Type    Description  
s_coord-4 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=s1.5 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s_coord-5The COMBINE action with label s_coord-5 calculates the following quantities: Quantity    Type    Description  
s_coord-5 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=s1.6 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s_coord-6The COMBINE action with label s_coord-6 calculates the following quantities: Quantity    Type    Description  
s_coord-6 scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=s1.7 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=s.* FILEthe name of the file on which to output these quantities=colvar

Full list of keywords

The following table describes the keywords and options that can be used with this action

Keyword	Type	Default	Description
MATRIX	optional	not used	the matrix that you would like to perform SPRINT on
GROUP	optional	not used	specifies the list of atoms that should be assumed indistinguishable
SWITCH	optional	not used	specify the switching function to use between two sets of indistinguishable atoms

References

More information about how this action can be used is available in the following articles:

F. Pietrucci, W. Andreoni, Graph Theory MeetsAb InitioMolecular Dynamics: Atomic Structures and Transformations at the Nanoscale. Physical Review Letters. 107 (2011)

Quantity	Type	Description
ss_jmat	matrix	a matrix containing the weights for the bonds between each pair of atoms