Shortcut: LOCAL_AVERAGE

Module	symfunc
Description	Usage
Calculate averages over spherical regions centered on atoms
output value	type
the values of the local averages	vector

Output components

This action can calculate the values in the following table when the associated keyword is included in the input for the action. These values can be referenced elsewhere in the input by using this Action's label followed by a dot and the name of the value required from the list below.

Name	Type	Keyword	Description
lessthan	scalar	LESS_THAN	the number of colvars that have a value less than a threshold
morethan	scalar	MORE_THAN	the number of colvars that have a value more than a threshold
altmin	scalar	ALT_MIN	the minimum value of the cv
min	scalar	MIN	the minimum colvar
max	scalar	MAX	the maximum colvar
between	scalar	BETWEEN	the number of colvars that have a value that lies in a particular interval
highest	scalar	HIGHEST	the largest of the colvars
lowest	scalar	LOWEST	the smallest of the colvars
sum	scalar	SUM	the sum of the colvars
mean	scalar	MEAN	the mean of the colvars

Input

The atoms that serve as the input for this action are specified using one or more of the keywords in the following table.

Keyword	Type	Description
SPECIES	atoms	the list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments
SPECIESA	atoms	the list of atoms for which the symmetry function is being calculated
SPECIESB	atoms	the list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated

Further details and examples

Calculate averages over spherical regions centered on atoms

As is explained in this video certain PLUMED actions calculate one scalar quantity or one vector for each of the atoms in the system. For example COORDINATIONNUMBER measures the coordination number of each of the atoms in the system and Q4 measures the 4th order Steinhardt parameter for each of the atoms in the system. These quantities provide tell us something about the disposition of the atoms in the first coordination sphere of each of the atoms of interest. In the paper in the bibliography Lechner and Dellago have suggested that one can probe local order in a system by taking the average value of such symmetry functions over the atoms within a spherical cutoff of each of these atoms in the systems. When this is done with Steinhardt parameters they claim this gives a coordinate that is better able to distinguish solid and liquid configurations of Lennard-Jones atoms.

You can calculate such locally averaged quantities within plumed by using the LOCAL_AVERAGE command. This command calculates the following atom-centered quantities:

$s_i = \frac{ c_i + \sum_j \sigma(r_{ij})c_j }{ 1 + \sum_j \sigma(r_{ij}) }$

where the $c_i$ and $c_j$ values can be any vector of symmetry functions that can be calculated using plumed multicolvars. The function $\sigma( r_{ij} )$ is a switching function that acts on the distance between atoms $i$ and $j$ . Lechner and Dellago suggest that the parameters of this function should be set so that it the function is equal to one when atom $j$ is in the first coordination sphere of atom $i$ and is zero otherwise.

To see how this works in practice consider the following example input.

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

d1The COORDINATIONNUMBER action with label d1 calculates the following quantities: Quantity    Type    Description  
d1 vector the coordination numbers of the specified atoms: COORDINATIONNUMBERCalculate the coordination numbers of atoms so that you can then calculate functions of the distribution of This action is a shortcut and it has hidden defaults. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=1-64 D_0 The d_0 parameter of the switching function=1.3 R_0The r_0 parameter of the switching function=0.2
d1: COORDINATIONNUMBERCalculate the coordination numbers of atoms so that you can then calculate functions of the distribution of This action is a shortcut and uses the defaults shown here. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=1-64 D_0 The d_0 parameter of the switching function=1.3 R_0The r_0 parameter of the switching function=0.2  NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0
# PLUMED interprets the command:
# d1: COORDINATIONNUMBER SPECIES=1-64 D_0=1.3 R_0=0.2
# as follows (Click the red comment above to revert to the short version of the input):
d1_grpThe GROUP action with label d1_grp calculates the following quantities: Quantity    Type    Description  
d1_grp atoms indices of atoms specified in GROUP: GROUPDefine a group of atoms so that a particular list of atoms can be referenced with a single label in definitions of CVs or virtual atoms. More details ATOMSthe numerical indexes for the set of atoms in the group=1-64
d1_matThe CONTACT_MATRIX action with label d1_mat calculates the following quantities: Quantity    Type    Description  
d1_mat 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=1-64 R_0The r_0 parameter of the switching function=0.2 D_0 The d_0 parameter of the switching function=1.3 NN The n parameter of the switching function =6 MM The m parameter of the switching function; 0 implies 2*NN=0
d1_onesThe CONSTANT action with label d1_ones calculates the following quantities: Quantity    Type    Description  
d1_ones vector the constant value that was read from the plumed input: ONESCreate a constant vector with all elements equal to one More details SIZEthe number of ones that you would like to create=64
d1The MATRIX_VECTOR_PRODUCT action with label d1 calculates the following quantities: Quantity    Type    Description  
d1 vector the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details  ARGthe label for the matrix and the vector/scalar that are being multiplied=d1_mat,d1_ones
d1_caverageThe MEAN action with label d1_caverage calculates the following quantities: Quantity    Type    Description  
d1_caverage scalar the mean of all the elements in the input vector: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe values input to this function=d1 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- laThe LOCAL_AVERAGE action with label la calculates the following quantities: Quantity    Type    Description  
la vector the values of the local averages
la_morethan scalar the number of colvars that have a value more than a threshold: LOCAL_AVERAGECalculate averages over spherical regions centered on atoms This action is a shortcut. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=d1 SWITCHthe switching function that it used in the construction of the contact matrix. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL D_0=1.3 R_0=0.2} MORE_THANcalculate the number of variables that are more than a certain target value. Options for this keyword are explained in the documentation for MORE_THAN.={RATIONAL R_0=4}
# PLUMED interprets the command:
# la: LOCAL_AVERAGE SPECIES=d1 SWITCH={RATIONAL D_0=1.3 R_0=0.2} MORE_THAN={RATIONAL R_0=4}
# as follows (Click the red comment above to revert to the short version of the input):
la_grpThe GROUP action with label la_grp calculates the following quantities: Quantity    Type    Description  
la_grp atoms indices of atoms specified in GROUP: GROUPDefine a group of atoms so that a particular list of atoms can be referenced with a single label in definitions of CVs or virtual atoms. More details ATOMSthe numerical indexes for the set of atoms in the group=d1
la_matThe CONTACT_MATRIX action with label la_mat calculates the following quantities: Quantity    Type    Description  
la_mat 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=d1 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 D_0=1.3 R_0=0.2}
la_onesThe CONSTANT action with label la_ones calculates the following quantities: Quantity    Type    Description  
la_ones vector the constant value that was read from the plumed input: ONESCreate a constant vector with all elements equal to one More details SIZEthe number of ones that you would like to create=64
la_coordThe MATRIX_VECTOR_PRODUCT action with label la_coord calculates the following quantities: Quantity    Type    Description  
la_coord vector the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details ARGthe label for the matrix and the vector/scalar that are being multiplied=la_mat,la_ones
la_prodThe MATRIX_VECTOR_PRODUCT action with label la_prod calculates the following quantities: Quantity    Type    Description  
la_prod vector the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details ARGthe label for the matrix and the vector/scalar that are being multiplied=la_mat,d1 
laThe CUSTOM action with label la calculates the following quantities: Quantity    Type    Description  
la 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=la_prod,d1,la_coord  FUNCthe function you wish to evaluate=(x+y)/(1+z) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
la_mtThe MORE_THAN action with label la_mt calculates the following quantities: Quantity    Type    Description  
la_mt vector the vector obtained by doing an element-wise application of a function that is one if the if the input is more than a threshold to the input vectors: MORE_THANUse a switching function to determine how many of the input variables are more than a certain cutoff. More details ARGthe values input to this function=la SWITCHThis keyword is used if you want to employ an alternative to the continuous swiching function defined above={RATIONAL R_0=4}
la_morethanThe SUM action with label la_morethan calculates the following quantities: Quantity    Type    Description  
la_morethan scalar the sum of all the elements in the input vector: SUMCalculate the sum of the arguments More details ARGthe values input to this function=la_mt 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=la.* FILEthe name of the file on which to output these quantities=colvar

This input calculates the coordination numbers for all the atoms in the system. These coordination numbers are then averaged over spherical regions. The number of averaged coordination numbers that are greater than 4 is then output to a file. Furthermore, if you expand the input above you can see how the LOCAL_AVERAGE command is a shortcut action that expands to a longer input that you should be able to interpret.

What Lechner and Dellago did in their paper was a little more complicated than this first example. To reproduce what they did you would use an input something like this:

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

Q4Calculate fourth order Steinhardt parameters. This action is a shortcut. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=1-64 SWITCHthe switching function that it used in the construction of the contact matrix. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL D_0=1.3 R_0=0.2} LABELa label for the action so that its output can be referenced in the input to other actions=q4The Q4 action with label q4 calculates the following quantities: Quantity    Type    Description  
q4 vector the norms of the vectors of spherical harmonic coefficients
# PLUMED interprets the command:
# Q4 SPECIES=1-64 SWITCH={RATIONAL D_0=1.3 R_0=0.2} LABEL=q4
# as follows (Click the red comment above to revert to the short version of the input):
q4_grpThe GROUP action with label q4_grp calculates the following quantities: Quantity    Type    Description  
q4_grp atoms indices of atoms specified in GROUP: GROUPDefine a group of atoms so that a particular list of atoms can be referenced with a single label in definitions of CVs or virtual atoms. More details ATOMSthe numerical indexes for the set of atoms in the group=1-64
q4_matThe CONTACT_MATRIX action with label q4_mat calculates the following quantities: Quantity    Type    Description  
q4_mat.w matrix a matrix containing the weights for the bonds between each pair of atoms
q4_mat.x matrix the projection of the bond on the x axis
q4_mat.y matrix the projection of the bond on the y axis
q4_mat.z matrix the projection of the bond on the z axis: 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=1-64 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 D_0=1.3 R_0=0.2} COMPONENTS also calculate the components of the vectors connecting the atoms in the contact matrix
q4_shThe SPHERICAL_HARMONIC action with label q4_sh calculates the following quantities: Quantity    Type    Description  
q4_sh.rm-n4 matrix the real parts of the spherical harmonic values with the m value given  This is the n4th of these quantities
q4_sh.rm-n3 matrix the real parts of the spherical harmonic values with the m value given  This is the n3th of these quantities
q4_sh.rm-n2 matrix the real parts of the spherical harmonic values with the m value given  This is the n2th of these quantities
q4_sh.rm-n1 matrix the real parts of the spherical harmonic values with the m value given  This is the n1th of these quantities
q4_sh.rm-0 matrix the real parts of the spherical harmonic values with the m value given  This is the 0th of these quantities
q4_sh.rm-p1 matrix the real parts of the spherical harmonic values with the m value given  This is the p1th of these quantities
q4_sh.rm-p2 matrix the real parts of the spherical harmonic values with the m value given  This is the p2th of these quantities
q4_sh.rm-p3 matrix the real parts of the spherical harmonic values with the m value given  This is the p3th of these quantities
q4_sh.rm-p4 matrix the real parts of the spherical harmonic values with the m value given  This is the p4th of these quantities
q4_sh.im-n4 matrix the real parts of the spherical harmonic values with the m value given  This is the n4th of these quantities
q4_sh.im-n3 matrix the real parts of the spherical harmonic values with the m value given  This is the n3th of these quantities
q4_sh.im-n2 matrix the real parts of the spherical harmonic values with the m value given  This is the n2th of these quantities
q4_sh.im-n1 matrix the real parts of the spherical harmonic values with the m value given  This is the n1th of these quantities
q4_sh.im-0 matrix the real parts of the spherical harmonic values with the m value given  This is the 0th of these quantities
q4_sh.im-p1 matrix the real parts of the spherical harmonic values with the m value given  This is the p1th of these quantities
q4_sh.im-p2 matrix the real parts of the spherical harmonic values with the m value given  This is the p2th of these quantities
q4_sh.im-p3 matrix the real parts of the spherical harmonic values with the m value given  This is the p3th of these quantities
q4_sh.im-p4 matrix the real parts of the spherical harmonic values with the m value given  This is the p4th of these quantities: SPHERICAL_HARMONICCalculate the values of all the spherical harmonic funtions for a particular value of l. More details ARGthe values input to this function=q4_mat.x,q4_mat.y,q4_mat.z,q4_mat.w Lthe value of the angular momentum=4
q4_denom_onesThe CONSTANT action with label q4_denom_ones calculates the following quantities: Quantity    Type    Description  
q4_denom_ones vector the constant value that was read from the plumed input: ONESCreate a constant vector with all elements equal to one More details SIZEthe number of ones that you would like to create=64
q4_denomThe MATRIX_VECTOR_PRODUCT action with label q4_denom calculates the following quantities: Quantity    Type    Description  
q4_denom vector the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details ARGthe label for the matrix and the vector/scalar that are being multiplied=q4_mat.w,q4_denom_ones
q4_spThe MATRIX_VECTOR_PRODUCT action with label q4_sp calculates the following quantities: Quantity    Type    Description  
q4_sp.rm-n4 vector the product of the matrix q4_sh.rm-n4 and the vector q4_denom_ones
q4_sp.rm-n3 vector the product of the matrix q4_sh.rm-n3 and the vector q4_denom_ones
q4_sp.rm-n2 vector the product of the matrix q4_sh.rm-n2 and the vector q4_denom_ones
q4_sp.rm-n1 vector the product of the matrix q4_sh.rm-n1 and the vector q4_denom_ones
q4_sp.rm-0 vector the product of the matrix q4_sh.rm-0 and the vector q4_denom_ones
q4_sp.rm-p1 vector the product of the matrix q4_sh.rm-p1 and the vector q4_denom_ones
q4_sp.rm-p2 vector the product of the matrix q4_sh.rm-p2 and the vector q4_denom_ones
q4_sp.rm-p3 vector the product of the matrix q4_sh.rm-p3 and the vector q4_denom_ones
q4_sp.rm-p4 vector the product of the matrix q4_sh.rm-p4 and the vector q4_denom_ones
q4_sp.im-n4 vector the product of the matrix q4_sh.im-n4 and the vector q4_denom_ones
q4_sp.im-n3 vector the product of the matrix q4_sh.im-n3 and the vector q4_denom_ones
q4_sp.im-n2 vector the product of the matrix q4_sh.im-n2 and the vector q4_denom_ones
q4_sp.im-n1 vector the product of the matrix q4_sh.im-n1 and the vector q4_denom_ones
q4_sp.im-0 vector the product of the matrix q4_sh.im-0 and the vector q4_denom_ones
q4_sp.im-p1 vector the product of the matrix q4_sh.im-p1 and the vector q4_denom_ones
q4_sp.im-p2 vector the product of the matrix q4_sh.im-p2 and the vector q4_denom_ones
q4_sp.im-p3 vector the product of the matrix q4_sh.im-p3 and the vector q4_denom_ones
q4_sp.im-p4 vector the product of the matrix q4_sh.im-p4 and the vector q4_denom_ones: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details ARGthe label for the matrix and the vector/scalar that are being multiplied=q4_sh.*,q4_denom_ones
q4_norm2The COMBINE action with label q4_norm2 calculates the following quantities: Quantity    Type    Description  
q4_norm2 vector the vector obtained by doing an element-wise application of a linear compbination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO POWERS the powers to which you are raising each of the arguments in your function=2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2 ARGthe values input to this function=q4_sp.rm-n4,q4_sp.im-n4,q4_sp.rm-n3,q4_sp.im-n3,q4_sp.rm-n2,q4_sp.im-n2,q4_sp.rm-n1,q4_sp.im-n1,q4_sp.rm-0,q4_sp.im-0,q4_sp.rm-p1,q4_sp.im-p1,q4_sp.rm-p2,q4_sp.im-p2,q4_sp.rm-p3,q4_sp.im-p3,q4_sp.rm-p4,q4_sp.im-p4
q4_normThe CUSTOM action with label q4_norm calculates the following quantities: Quantity    Type    Description  
q4_norm 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=q4_norm2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4The CUSTOM action with label q4 calculates the following quantities: Quantity    Type    Description  
q4 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=q4_norm,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- LOCAL_AVERAGECalculate averages over spherical regions centered on atoms This action is a shortcut. More details SPECIESthe list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments=q4 SWITCHthe switching function that it used in the construction of the contact matrix. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL D_0=1.3 R_0=0.2} MEAN calculate the mean of all the quantities LABELa label for the action so that its output can be referenced in the input to other actions=laThe LOCAL_AVERAGE action with label la calculates the following quantities: Quantity    Type    Description  
la vector the values of the local averages
la_mean scalar the mean of the colvars
# PLUMED interprets the command:
# LOCAL_AVERAGE SPECIES=q4 SWITCH={RATIONAL D_0=1.3 R_0=0.2} MEAN LABEL=la
# as follows (Click the red comment above to revert to the short version of the input):
la_grpThe GROUP action with label la_grp calculates the following quantities: Quantity    Type    Description  
la_grp atoms indices of atoms specified in GROUP: GROUPDefine a group of atoms so that a particular list of atoms can be referenced with a single label in definitions of CVs or virtual atoms. More details ATOMSthe numerical indexes for the set of atoms in the group=q4
la_matThe CONTACT_MATRIX action with label la_mat calculates the following quantities: Quantity    Type    Description  
la_mat 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=q4 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 D_0=1.3 R_0=0.2}
la_onesThe CONSTANT action with label la_ones calculates the following quantities: Quantity    Type    Description  
la_ones vector the constant value that was read from the plumed input: ONESCreate a constant vector with all elements equal to one More details SIZEthe number of ones that you would like to create=64
la_coordThe MATRIX_VECTOR_PRODUCT action with label la_coord calculates the following quantities: Quantity    Type    Description  
la_coord vector the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details ARGthe label for the matrix and the vector/scalar that are being multiplied=la_mat,la_ones
q4_rmn-n4The CUSTOM action with label q4_rmn-n4 calculates the following quantities: Quantity    Type    Description  
q4_rmn-n4 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=q4_sp.rm-n4,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_imn-n4The CUSTOM action with label q4_imn-n4 calculates the following quantities: Quantity    Type    Description  
q4_imn-n4 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=q4_sp.im-n4,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_rmn-n3The CUSTOM action with label q4_rmn-n3 calculates the following quantities: Quantity    Type    Description  
q4_rmn-n3 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=q4_sp.rm-n3,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_imn-n3The CUSTOM action with label q4_imn-n3 calculates the following quantities: Quantity    Type    Description  
q4_imn-n3 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=q4_sp.im-n3,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_rmn-n2The CUSTOM action with label q4_rmn-n2 calculates the following quantities: Quantity    Type    Description  
q4_rmn-n2 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=q4_sp.rm-n2,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_imn-n2The CUSTOM action with label q4_imn-n2 calculates the following quantities: Quantity    Type    Description  
q4_imn-n2 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=q4_sp.im-n2,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_rmn-n1The CUSTOM action with label q4_rmn-n1 calculates the following quantities: Quantity    Type    Description  
q4_rmn-n1 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=q4_sp.rm-n1,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_imn-n1The CUSTOM action with label q4_imn-n1 calculates the following quantities: Quantity    Type    Description  
q4_imn-n1 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=q4_sp.im-n1,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_rmn-0The CUSTOM action with label q4_rmn-0 calculates the following quantities: Quantity    Type    Description  
q4_rmn-0 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=q4_sp.rm-0,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_imn-0The CUSTOM action with label q4_imn-0 calculates the following quantities: Quantity    Type    Description  
q4_imn-0 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=q4_sp.im-0,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_rmn-p1The CUSTOM action with label q4_rmn-p1 calculates the following quantities: Quantity    Type    Description  
q4_rmn-p1 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=q4_sp.rm-p1,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_imn-p1The CUSTOM action with label q4_imn-p1 calculates the following quantities: Quantity    Type    Description  
q4_imn-p1 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=q4_sp.im-p1,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_rmn-p2The CUSTOM action with label q4_rmn-p2 calculates the following quantities: Quantity    Type    Description  
q4_rmn-p2 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=q4_sp.rm-p2,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_imn-p2The CUSTOM action with label q4_imn-p2 calculates the following quantities: Quantity    Type    Description  
q4_imn-p2 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=q4_sp.im-p2,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_rmn-p3The CUSTOM action with label q4_rmn-p3 calculates the following quantities: Quantity    Type    Description  
q4_rmn-p3 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=q4_sp.rm-p3,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_imn-p3The CUSTOM action with label q4_imn-p3 calculates the following quantities: Quantity    Type    Description  
q4_imn-p3 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=q4_sp.im-p3,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_rmn-p4The CUSTOM action with label q4_rmn-p4 calculates the following quantities: Quantity    Type    Description  
q4_rmn-p4 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=q4_sp.rm-p4,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
q4_imn-p4The CUSTOM action with label q4_imn-p4 calculates the following quantities: Quantity    Type    Description  
q4_imn-p4 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=q4_sp.im-p4,q4_denom FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
la_vstackThe VSTACK action with label la_vstack calculates the following quantities: Quantity    Type    Description  
la_vstack matrix a matrix that contains the input vectors in its columns: VSTACKCreate a matrix by stacking vectors together More details ARGthe values that you would like to stack together to construct the output matrix=q4_rmn-n4,q4_imn-n4,q4_rmn-n3,q4_imn-n3,q4_rmn-n2,q4_imn-n2,q4_rmn-n1,q4_imn-n1,q4_rmn-0,q4_imn-0,q4_rmn-p1,q4_imn-p1,q4_rmn-p2,q4_imn-p2,q4_rmn-p3,q4_imn-p3,q4_rmn-p4,q4_imn-p4
la_prodThe MATRIX_VECTOR_PRODUCT action with label la_prod calculates the following quantities: Quantity    Type    Description  
la_prod.q4_rmn-n4 vector the product of the matrix la_mat and the vector q4_rmn-n4
la_prod.q4_imn-n4 vector the product of the matrix la_mat and the vector q4_imn-n4
la_prod.q4_rmn-n3 vector the product of the matrix la_mat and the vector q4_rmn-n3
la_prod.q4_imn-n3 vector the product of the matrix la_mat and the vector q4_imn-n3
la_prod.q4_rmn-n2 vector the product of the matrix la_mat and the vector q4_rmn-n2
la_prod.q4_imn-n2 vector the product of the matrix la_mat and the vector q4_imn-n2
la_prod.q4_rmn-n1 vector the product of the matrix la_mat and the vector q4_rmn-n1
la_prod.q4_imn-n1 vector the product of the matrix la_mat and the vector q4_imn-n1
la_prod.q4_rmn-0 vector the product of the matrix la_mat and the vector q4_rmn-0
la_prod.q4_imn-0 vector the product of the matrix la_mat and the vector q4_imn-0
la_prod.q4_rmn-p1 vector the product of the matrix la_mat and the vector q4_rmn-p1
la_prod.q4_imn-p1 vector the product of the matrix la_mat and the vector q4_imn-p1
la_prod.q4_rmn-p2 vector the product of the matrix la_mat and the vector q4_rmn-p2
la_prod.q4_imn-p2 vector the product of the matrix la_mat and the vector q4_imn-p2
la_prod.q4_rmn-p3 vector the product of the matrix la_mat and the vector q4_rmn-p3
la_prod.q4_imn-p3 vector the product of the matrix la_mat and the vector q4_imn-p3
la_prod.q4_rmn-p4 vector the product of the matrix la_mat and the vector q4_rmn-p4
la_prod.q4_imn-p4 vector the product of the matrix la_mat and the vector q4_imn-p4: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details ARGthe label for the matrix and the vector/scalar that are being multiplied=la_mat,q4_rmn-n4,q4_imn-n4,q4_rmn-n3,q4_imn-n3,q4_rmn-n2,q4_imn-n2,q4_rmn-n1,q4_imn-n1,q4_rmn-0,q4_imn-0,q4_rmn-p1,q4_imn-p1,q4_rmn-p2,q4_imn-p2,q4_rmn-p3,q4_imn-p3,q4_rmn-p4,q4_imn-p4
la_vpstackThe VSTACK action with label la_vpstack calculates the following quantities: Quantity    Type    Description  
la_vpstack matrix a matrix that contains the input vectors in its columns: VSTACKCreate a matrix by stacking vectors together More details ARGthe values that you would like to stack together to construct the output matrix=la_prod.q4_rmn-n4,la_prod.q4_imn-n4,la_prod.q4_rmn-n3,la_prod.q4_imn-n3,la_prod.q4_rmn-n2,la_prod.q4_imn-n2,la_prod.q4_rmn-n1,la_prod.q4_imn-n1,la_prod.q4_rmn-0,la_prod.q4_imn-0,la_prod.q4_rmn-p1,la_prod.q4_imn-p1,la_prod.q4_rmn-p2,la_prod.q4_imn-p2,la_prod.q4_rmn-p3,la_prod.q4_imn-p3,la_prod.q4_rmn-p4,la_prod.q4_imn-p4
la_lonesThe CONSTANT action with label la_lones calculates the following quantities: Quantity    Type    Description  
la_lones vector the constant value that was read from the plumed input: ONESCreate a constant vector with all elements equal to one More details SIZEthe number of ones that you would like to create=18
la_unormThe OUTER_PRODUCT action with label la_unorm calculates the following quantities: Quantity    Type    Description  
la_unorm matrix a matrix containing the outer product of the two input vectors that was obtained using the function that was input: OUTER_PRODUCTCalculate the outer product matrix of two vectors More details ARGthe labels of the two vectors from which the outer product is being computed=la_coord,la_lones
la_avThe CUSTOM action with label la_av calculates the following quantities: Quantity    Type    Description  
la_av matrix the matrix obtained by doing an element-wise application of an arbitrary function to the input matrix: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=la_vpstack,la_vstack,la_unorm FUNCthe function you wish to evaluate=(x+y)/(1+z) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
la_av2The CUSTOM action with label la_av2 calculates the following quantities: Quantity    Type    Description  
la_av2 matrix the matrix obtained by doing an element-wise application of an arbitrary function to the input matrix: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=la_av FUNCthe function you wish to evaluate=x*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
la_2The MATRIX_VECTOR_PRODUCT action with label la_2 calculates the following quantities: Quantity    Type    Description  
la_2 vector the vector that is obtained by taking the product between the matrix and the vector that were input: MATRIX_VECTOR_PRODUCTCalculate the product of the matrix and the vector More details ARGthe label for the matrix and the vector/scalar that are being multiplied=la_av2,la_lones
laThe CUSTOM action with label la calculates the following quantities: Quantity    Type    Description  
la 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=la_2 FUNCthe function you wish to evaluate=sqrt(x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
la_meanThe MEAN action with label la_mean calculates the following quantities: Quantity    Type    Description  
la_mean scalar the mean of all the elements in the input vector: MEANCalculate the arithmetic mean of the elements in a vector More details ARGthe values input to this function=la 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=la.* FILEthe name of the file on which to output these quantities=colvar

This example input calculates the Q4 vectors for each of the atoms in the system. These vectors are then averaged component by component over a spherical region. The average value for this quantity is then outputeed to a file. If you want to understand more about the shortcut that is used here you can read this page.

References

More information about how this action can be used is available in the following articles: - A. D. White, G. A. Voth, Efficient and Minimal Method to Bias Molecular Simulations with Experimental Data. Journal of Chemical Theory and Computation. 10, 3023–3030 (2014) - W. Lechner, C. Dellago, Accurate determination of crystal structures based on averaged local bond order parameters. The Journal of Chemical Physics. 129 (2008)

Syntax

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

Keyword	Type	Default	Description
SPECIES	input	none	the list of atoms for which the symmetry function is being calculated and the atoms that can be in the environments
SPECIESA	input	none	the list of atoms for which the symmetry function is being calculated
SPECIESB	input	none	the list of atoms that can be in the environments of each of the atoms for which the symmetry function is being calculated
NN	compulsory	6	The n parameter of the switching function
MM	compulsory	0	The m parameter of the switching function; 0 implies 2*NN
D_0	compulsory	0.0	The d_0 parameter of the switching function
R_0	compulsory	none	The r_0 parameter of the switching function
SWITCH	optional	not used	the switching function that it used in the construction of the contact matrix. Options for this keyword are explained in the documentation for LESS_THAN.
LESS_THAN	optional	not used	calculate the number of variables that are less than a certain target value. Options for this keyword are explained in the documentation for LESS_THAN.
MORE_THAN	optional	not used	calculate the number of variables that are more than a certain target value. Options for this keyword are explained in the documentation for MORE_THAN.
ALT_MIN	optional	not used	calculate the minimum value
MIN	optional	not used	calculate the minimum value
MAX	optional	not used	calculate the maximum value
BETWEEN	optional	not used	calculate the number of values that are within a certain range. Options for this keyword are explained in the documentation for BETWEEN.
HIGHEST	optional	false	this flag allows you to recover the highest of these variables
HISTOGRAM	optional	not used	calculate a discretized histogram of the distribution of values
LOWEST	optional	false	this flag allows you to recover the lowest of these variables
SUM	optional	false	calculate the sum of all the quantities
MEAN	optional	false	calculate the mean of all the quantities

Quantity	Type	Description
d1	vector	the coordination numbers of the specified atoms