Shortcut: COMBINE

Module	function
Description	Usage
Calculate a polynomial combination of a set of other variables.
output value	type
a linear combination	scalar/vector/matrix

Details and examples

Calculate a polynomial combination of a set of other variables.

This action takes in $N_{arg}$ arguments ( $x_i$ ) and computes the following function of them:

$C=\sum_{i=1}^{N_{arg}} c_i (x_i-a_i)^{p_i}$

The $c_i$ , $a_i$ and $p_i$ values in this expression are provided through the COEFFICIENTS, PARAMETERS and POWERS keywords respectively. The following example illustrates how this action can be used to calculate and print the square of the distance between atom 1 and atom 2.

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

dThe DISTANCE action with label d calculates the following quantities: Quantity    Type    Description  
d.x scalar the x-component of the vector connecting the two atoms
d.y scalar the y-component of the vector connecting the two atoms
d.z scalar the z-component of the vector connecting the two atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,2 COMPONENTS calculate the x, y and z components of the distance separately and store them as label
cThe COMBINE action with label c calculates the following quantities: Quantity    Type    Description  
c scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=d.x,d.y,d.z COEFFICIENTS the coefficients of the arguments in your function=1,1,1 PARAMETERS the parameters of the arguments in your function=0,0,0 POWERS the powers to which you are raising each of the arguments in your function=2,2,2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c FILEthe name of the file on which to output these quantities=colvar

Notice that if the COEFFICIENTS keyword is absent all the $c_i$ values are set equal to 1. Furthermore, if the PARAMETERS keyword is absent all the $a_i$ values are set equal to 0. We can thus make use of these defaults and rewrite the input above as:

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

dThe DISTANCE action with label d calculates the following quantities: Quantity    Type    Description  
d.x scalar the x-component of the vector connecting the two atoms
d.y scalar the y-component of the vector connecting the two atoms
d.z scalar the z-component of the vector connecting the two atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,2 COMPONENTS calculate the x, y and z components of the distance separately and store them as label
cThe COMBINE action with label c calculates the following quantities: Quantity    Type    Description  
c scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=d.x,d.y,d.z POWERS the powers to which you are raising each of the arguments in your function=2,2,2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c FILEthe name of the file on which to output these quantities=colvar

Notice that we cannot remove the POWERS keyword here as if it is absent all the $p_i$ values are set equal to 1.

The NORMALIZE flag

Using the NORAMALIZE flag in the input below ensures that the coefficients of the three input scalars are all set equal to one:

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

dThe DISTANCE action with label d calculates the following quantities: Quantity    Type    Description  
d.x scalar the x-component of the vector connecting the two atoms
d.y scalar the y-component of the vector connecting the two atoms
d.z scalar the z-component of the vector connecting the two atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,2 COMPONENTS calculate the x, y and z components of the distance separately and store them as label
cThe COMBINE action with label c calculates the following quantities: Quantity    Type    Description  
c scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=d.x,d.y,d.z NORMALIZE normalize all the coefficients so that in total they are equal to one PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c FILEthe name of the file on which to output these quantities=colvar

Notice that you can use this flag together with the coefficient keyword as shown below:

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

dThe DISTANCE action with label d calculates the following quantities: Quantity    Type    Description  
d.x scalar the x-component of the vector connecting the two atoms
d.y scalar the y-component of the vector connecting the two atoms
d.z scalar the z-component of the vector connecting the two atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,2 COMPONENTS calculate the x, y and z components of the distance separately and store them as label
cThe COMBINE action with label c calculates the following quantities: Quantity    Type    Description  
c scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=d.x,d.y,d.z NORMALIZE normalize all the coefficients so that in total they are equal to one COEFFICIENTS the coefficients of the arguments in your function=2,1,3 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c FILEthe name of the file on which to output these quantities=colvar

The coefficients of d.x, d.y and d.z for this input are 1/3, 1/6 and 1/2 respectively.

Periodic arguments

The COMBINE action is not able to predict the periodic domain for the function that is computed from the arguments automatically. The user is thus forced to specify it explicitly. Use PERIODIC=NO if the resulting variable is not periodic, and PERIODIC=A,B where A and B are the two boundaries for the periodic domain if the resulting variable is periodic. The following provides an example where the output from combine has a periodic domain. In this input we are taking the cube of a dihedral angle. The dihedral angle has a periodic domain that runs from $-\pi$ to $\pi$ . The cube of this variable thus has a periodic domain that runs from $-\pi^3$ to $\pi^3$ as indicated in the following input.

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

tThe TORSION action with label t calculates the following quantities: Quantity    Type    Description  
t scalar the TORSION involving these atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMSthe four atoms involved in the torsional angle=1,3,5,7
#c: COMBINE ARG=t POWERS=3 PERIODIC=-31.0062766802998,31.0062766802998
cThe COMBINE action with label c calculates the following quantities: Quantity    Type    Description  
c scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=t POWERS the powers to which you are raising each of the arguments in your function=3 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=-pi^3,pi^3
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c FILEthe name of the file on which to output these quantities=colvar

Vector arguments

The two examples in the previous section demonstrate how to use the COMBINE action with scalar arguments. However, you can also pass arguments to this action that have a rank greater than zero. For example, in the example below COMBINE accepts three vectors with 4 elements in input:

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

dThe DISTANCE action with label d calculates the following quantities: Quantity    Type    Description  
d.x vector the x-component of the vector connecting the two atoms
d.y vector the y-component of the vector connecting the two atoms
d.z vector the z-component of the vector connecting the two atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=1,2 ATOMS2the pair of atom that we are calculating the distance between=3,4 ATOMS3the pair of atom that we are calculating the distance between=5,6 ATOMS4the pair of atom that we are calculating the distance between=7,8 COMPONENTS calculate the x, y and z components of the distance separately and store them as label
cThe COMBINE action with label c calculates the following quantities: Quantity    Type    Description  
c vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=d.x,d.y,d.z POWERS the powers to which you are raising each of the arguments in your function=2,2,2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c FILEthe name of the file on which to output these quantities=colvar

The output from the COMBINE action here is also a vector with four elements. The first element of this vector is the square of the distance betwen atoms 1 and 2, the second is the square of the distance between atoms 3 and 4 and so on.

The COMBINE action can also take a mixture of scalars and vectors in input as long as the labels of vectors appear before the labels of scalars in the input to the ARG keyword. The following input illustrates an COMBINE action that takes vectors and scalars in input.

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

pThe CONSTANT action with label p calculates the following quantities: Quantity    Type    Description  
p scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions This action has hidden defaults. More details VALUEthe single number that you would like to store=2
p: CONSTANTCreate a constant value that can be passed to actions This action uses the defaults shown here. More details VALUEthe single number that you would like to store=2  NROWS the number of rows in your input matrix=0 NCOLS the number of columns in your matrix=0
dThe DISTANCE action with label d calculates the following quantities: Quantity    Type    Description  
d vector the DISTANCE for each set of specified atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=1,2 ATOMS2the pair of atom that we are calculating the distance between=3,4 ATOMS3the pair of atom that we are calculating the distance between=5,6 ATOMS4the pair of atom that we are calculating the distance between=7,8
cThe COMBINE action with label c calculates the following quantities: Quantity    Type    Description  
c vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=d,p COEFFICIENTS the coefficients of the arguments in your function=4,-1 POWERS the powers to which you are raising each of the arguments in your function=2.5,1 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c FILEthe name of the file on which to output these quantities=colvar

The elements of the vector that is calculated by the COMBINE action here are given by:

$c_i = 4d_i^{2.5} - 2$

The $d_i$ in this expression are the distances that were calculated by the DISTANCE action. The 2 comes from the scalar p that passed to the ARG action in input. As a single scalar is passed the same number is used when calculating all 4 elements of the output vector. In other words, the scalar behaves as if it is a vector with four components that all have the same value.

Lastly, notice that if you pass a single vector in input to COMBINE as in the following example, the output is still a vector:

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

dThe DISTANCE action with label d calculates the following quantities: Quantity    Type    Description  
d vector the DISTANCE for each set of specified atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=1,2 ATOMS2the pair of atom that we are calculating the distance between=3,4 ATOMS3the pair of atom that we are calculating the distance between=5,6 ATOMS4the pair of atom that we are calculating the distance between=7,8
cThe COMBINE action with label c calculates the following quantities: Quantity    Type    Description  
c vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=d COEFFICIENTS the coefficients of the arguments in your function=4 POWERS the powers to which you are raising each of the arguments in your function=2.5 PARAMETERS the parameters of the arguments in your function=0.5 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c FILEthe name of the file on which to output these quantities=colvar

To calculate the 4-dimensional output by the COMBINE action here we subtract 0.5 from each of the input distances, raise the result from this subtraction to the power 2.5 and then multiply the result by 4.

If you want to calculate a linear combination of the elements of a vector using the formula at the top of the page you should use the CUSTOM action to transform all the components of the input vector. You can then add all the results from these transformations together using SUM.

Matrix arguments

You can also use matrices in the input to the COMBINE action as illustrated below:

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

dThe DISTANCE_MATRIX action with label d calculates the following quantities: Quantity    Type    Description  
d.w matrix a matrix containing the weights for the bonds between each pair of atoms
d.x matrix the projection of the bond on the x axis
d.y matrix the projection of the bond on the y axis
d.z matrix the projection of the bond on the z axis: DISTANCE_MATRIXCalculate a matrix of distances between atoms. This action has hidden defaults. More details GROUPAwhen you are calculating the adjacency matrix between two sets of atoms this keyword is used to specify the atoms along with the keyword GROUPB=1,2 GROUPBwhen you are calculating the adjacency matrix between two sets of atoms this keyword is used to specify the atoms along with the keyword GROUPA=3,4,5 COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
d: DISTANCE_MATRIXCalculate a matrix of distances between atoms. This action uses the defaults shown here. More details GROUPAwhen you are calculating the adjacency matrix between two sets of atoms this keyword is used to specify the atoms along with the keyword GROUPB=1,2 GROUPBwhen you are calculating the adjacency matrix between two sets of atoms this keyword is used to specify the atoms along with the keyword GROUPA=3,4,5 COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix  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 CUTOFF ignore distances that have a value larger than this cutoff=-1
cThe COMBINE action with label c calculates the following quantities: Quantity    Type    Description  
c matrix the matrix obtained by doing an element-wise application of a linear combination to the input matrix: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=d.x,d.y,d.z POWERS the powers to which you are raising each of the arguments in your function=2,2,2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c FILEthe name of the file on which to output these quantities=colvar

The input to the combine action here consists of three $2\times3$ matrices. The output is thus a $2\times3$ matrix that contains the squares of the distances between the atoms in GROUPA and the atoms in GROUPB. Notice that all the input matrices must have the same size as the elements of the final matrix are calculated by applying the formula in the first section of this input to each set of elements to the input matrices in turn.

The input to this action can be a combination of matrices and scalars as long as the labels of the matrices appear before the labels of the scalars in the input for the ARG keyword. If your input arguments are an $N\times M$ matrix and a scalar the scalar is treated as if it is a $N\times M$ matrix which has all its elements equal to the input scalar. You cannot use a mixture of vectors and matrices in the input to this action.

Furthermore, if you pass a single matrix to COMBINE the output is a matrix. To calculate a linear combination of all the elements in a matrix using the formula at the top of the page you should use the CUSTOM action to transform all the components of the input vector. You can then add all the results from these transformations together using SUM.

The MASK keyword

The example input below illustrates a way you can use the MASK keyword to improve PLUMED performance for inputs that use COMBINE actions that take arguments that are vectors:

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

# Fixed virtual atom which serves as the probe volume's center (pos. in nm)
centerThe FIXEDATOM action with label center calculates the following quantities: Quantity    Type    Description  
center atoms virtual atom calculated by FIXEDATOM action: FIXEDATOMAdd a virtual atom in a fixed position. This action has hidden defaults. More details ATcoordinates of the virtual atom=2.5,2.5,2.5
center: FIXEDATOMAdd a virtual atom in a fixed position. This action uses the defaults shown here. More details ATcoordinates of the virtual atom=2.5,2.5,2.5  SET_MASS mass of the virtual atom=1 SET_CHARGE charge of the virtual atom=0
owThe GROUP action with label ow calculates the following quantities: Quantity    Type    Description  
ow 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=1-400
hwThe GROUP action with label hw calculates the following quantities: Quantity    Type    Description  
hw 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=401-1200
# Vector in which element i is one if atom i is in sphere of interest and zero otherwise
sphereThe INSPHERE action with label sphere calculates the following quantities: Quantity    Type    Description  
sphere vector vector of numbers between 0 and 1 that measure the degree to which each atom is within the volume of interest: INSPHEREThis quantity can be used to calculate functions of the distribution of collective variables for the atoms that lie in a particular, user-specified part of of the cell. More details ATOMSthe group of atoms that you would like to investigate=ow CENTERthe atom whose vicinity we are interested in examining=center RADIUSthe switching function that tells us the extent of the sphereical region of interest. Options for this keyword are explained in the documentation for LESS_THAN.={GAUSSIAN D_0=0.5 R_0=0.01 D_MAX=0.52}
# Calculate coordination with oxygen atoms
ow_onesThe ONES action with label ow_ones calculates the following quantities: Quantity    Type    Description  
ow_ones vector a vector of ones with the required number of elements: ONESCreate a constant vector with all elements equal to one This action is a shortcut. More details SIZEthe number of ones that you would like to create=400
# PLUMED interprets the command:
# ow_ones: ONES SIZE=400
# as follows (Click the red comment above to revert to the short version of the input):
ow_onesThe CONSTANT action with label ow_ones calculates the following quantities: Quantity    Type    Description  
ow_ones vector the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details NOLOG do not report all the read in scalars in the log VALUESthe numbers that are in your constant value=1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
# --- End of included input --- ow_matThe CONTACT_MATRIX action with label ow_mat calculates the following quantities: Quantity    Type    Description  
ow_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=ow MASKa vector that is used to used to determine which rows of the adjancency matrix to compute=sphere 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=0.3 D_MAX=0.8}
ow_coordThe MATRIX_VECTOR_PRODUCT action with label ow_coord calculates the following quantities: Quantity    Type    Description  
ow_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=ow_mat,ow_ones
# Calculate the coordination with hydrogen atoms
hw_onesThe ONES action with label hw_ones calculates the following quantities: Quantity    Type    Description  
hw_ones vector a vector of ones with the required number of elements: ONESCreate a constant vector with all elements equal to one This action is a shortcut. More details SIZEthe number of ones that you would like to create=800
# PLUMED interprets the command:
# hw_ones: ONES SIZE=800
# as follows (Click the red comment above to revert to the short version of the input):
hw_onesThe CONSTANT action with label hw_ones calculates the following quantities: Quantity    Type    Description  
hw_ones vector the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details NOLOG do not report all the read in scalars in the log VALUESthe numbers that are in your constant value=1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
# --- End of included input --- hw_matThe CONTACT_MATRIX action with label hw_mat calculates the following quantities: Quantity    Type    Description  
hw_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 GROUPAwhen you are calculating the adjacency matrix between two sets of atoms this keyword is used to specify the atoms along with the keyword GROUPB=ow GROUPBwhen you are calculating the adjacency matrix between two sets of atoms this keyword is used to specify the atoms along with the keyword GROUPA=hw MASKa vector that is used to used to determine which rows of the adjancency matrix to compute=sphere 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 D_MAX=0.5}
hw_coordThe MATRIX_VECTOR_PRODUCT action with label hw_coord calculates the following quantities: Quantity    Type    Description  
hw_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=hw_mat,hw_ones
# And do the linear combination of the transformed coordination numbers together
prodThe COMBINE action with label prod calculates the following quantities: Quantity    Type    Description  
prod vector the vector obtained by doing an element-wise application of a linear combination to the input vectors: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=hw_coord,ow_coord COEFFICIENTS the coefficients of the arguments in your function=2,8 MASKthe label for a sparse vector/matrix that should be used to determine which elements of the vector/matrix should be computed=sphere PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# Sum of coordination numbers for atoms that are in the sphere of interest
numerThe SUM action with label numer calculates the following quantities: Quantity    Type    Description  
numer scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=prod PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
denomThe SUM action with label denom calculates the following quantities: Quantity    Type    Description  
denom scalar the SUM of the elements in the input value: SUMCalculate the sum of the arguments More details ARGthe vector/matrix/grid whose elements shuld be added together=sphere PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
cvThe CUSTOM action with label cv calculates the following quantities: Quantity    Type    Description  
cv scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=numer,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
# And print out final CV to a file
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=cv FILEthe name of the file on which to output these quantities=colvar STRIDE the frequency with which the quantities of interest should be output=1

The variable being computed is computed for the oxygen atoms in a spherical region centered on the point $(2.5,2.5,2.5)$ and is a linear combination of the coordination number of the atoms in this region with the oxygen atoms and the coordination number of the atoms in this region with the hydrogen atoms. The average value of this linear combination for the atoms that are within this region is output.

If the arguments input to the COMBINE action are matrices then the MASK keyword is used in the way that is described in the documentation for the CUSTOM.

Input

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

Keyword	Type	Description
ARG	scalar/vector/matrix	the values input to this function
MASK	vector/matrix	the label for a sparse vector/matrix that should be used to determine which elements of the vector/matrix should be computed

Full list of keywords

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

Keyword	Type	Default	Description
ARG	input	none	the values input to this function
MASK	input	none	the label for a sparse vector/matrix that should be used to determine which elements of the vector/matrix should be computed
PERIODIC	compulsory	none	if the output of your function is periodic then you should specify the periodicity of the function
COEFFICIENTS	compulsory	1.0	the coefficients of the arguments in your function
PARAMETERS	compulsory	0.0	the parameters of the arguments in your function
POWERS	compulsory	1.0	the powers to which you are raising each of the arguments in your function
NORMALIZE	optional	false	normalize all the coefficients so that in total they are equal to one

Quantity	Type	Description
d.x	scalar	the x-component of the vector connecting the two atoms
d.y	scalar	the y-component of the vector connecting the two atoms
d.z	scalar	the z-component of the vector connecting the two atoms