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PLUMED manual

Shortcut: KERNEL

Shortcut: KERNEL

Module	refdist
Description	Usage
Transform a set of input coordinates using a kernel function
output value	type
the value of the kernel evaluated at the argument values	scalar/vector

Details and examples

Transform a set of input coordinates using a kernel function

This action takes a vector of arguments in input, $s$ , the square of the NORMALIZED_EUCLIDEAN_DISTANCE or MAHALANOBIS_DISTANCE between the instataneous values of these arguments and a set of reference values for them is then computed. If this squared distance is $x$ then the final quantity that is returned by this function is:

$f = w K(x)$

where $w$ is a scalar that the user specifies using the WEIGHT keyword and $K$ can be a function of $x$ that the user specifies using the FUNC keyword or one of the Kernel functions options from the following table that are available internally:

Instruction	Function
FUNC=gaussian	$\exp(-x/2)$
FUNC=von-misses	$\exp(-x/2)$
FUNC=triangular	$1-\sqrt{x} \quad \textrm{if} \quad x<1 \quad \textrm{otherwise} \quad 0$

The von-misses options here is used if the input arguments have a periodic domain. This instruction changes the way the MAHALANOBIS_DISTANCE is computed so that the method that is appropriate for using with periodic variables is employed in place of the default method.

Examples

The following example demonstrates how this action can be used to evaluate a Kernel that is a function of one argument:

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 scalar the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,2
kThe KERNEL action with label k calculates the following quantities: Quantity    Type    Description  
k scalar the value of the kernel evaluated at the argument values: KERNELTransform a set of input coordinates using a kernel function This action is a shortcut and it has hidden defaults. More details ARGthe arguments that should be used as input to this method=d TYPE the type of kernel to use=gaussian CENTERthe position of the center of the kernel=1 SIGMAsquare root of variance of the cluster=0.1
k: KERNELTransform a set of input coordinates using a kernel function This action is a shortcut and uses the defaults shown here. More details ARGthe arguments that should be used as input to this method=d TYPE the type of kernel to use=gaussian CENTERthe position of the center of the kernel=1 SIGMAsquare root of variance of the cluster=0.1  WEIGHT the weight to multiply this kernel function by=1.0
# PLUMED interprets the command:
# k: KERNEL ARG=d TYPE=gaussian CENTER=1 SIGMA=0.1
# as follows (Click the red comment above to revert to the short version of the input):
k_d_refThe CONSTANT action with label k_d_ref calculates the following quantities: Quantity    Type    Description  
k_d_ref scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=1
k_sigmaThe CONSTANT action with label k_sigma calculates the following quantities: Quantity    Type    Description  
k_sigma scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=0.1
k_varThe CUSTOM action with label k_var calculates the following quantities: Quantity    Type    Description  
k_var scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=k_sigma 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
k_icovThe CUSTOM action with label k_icov calculates the following quantities: Quantity    Type    Description  
k_icov scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=k_var FUNCthe function you wish to evaluate=1/x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
k_dist_2The MATRIX_PRODUCT_DIAGONAL action with label k_dist_2 calculates the following quantities: Quantity    Type    Description  
k_dist_2 scalar a vector containing the diagonal elements of the matrix that obtaned by multiplying the two input matrices together: NORMALIZED_EUCLIDEAN_DISTANCECalculate the normalised euclidean distance between two points in CV space More details SQUARED The squared distance should be calculated ARG1The poin that we are calculating the distance from=d ARG2The point that we are calculating the distance to=k_d_ref METRICThe inverse covariance matrix that should be used when calculating the distance=k_icov
kThe CUSTOM action with label k calculates the following quantities: Quantity    Type    Description  
k scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=k_dist_2 FUNCthe function you wish to evaluate=1.0*exp(-x/2) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input ---

The NORMALIZED_EUCLIDEAN_DISTANCE between the instantaneous distance and the point 1 is evaluated here. The metric vector that is used to evaluate this distance is taking the reciprocal of the square of the input SIGMA value. Lastly, the height of the Gaussian, $w$ , in the expression above is set equal to one. If you would like the total volume of the Gaussian to be equal to one you use the NORMALIZED keyword as shown here:

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 scalar the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,2
kThe KERNEL action with label k calculates the following quantities: Quantity    Type    Description  
k scalar the value of the kernel evaluated at the argument values: KERNELTransform a set of input coordinates using a kernel function This action is a shortcut and it has hidden defaults. More details ARGthe arguments that should be used as input to this method=d TYPE the type of kernel to use=gaussian CENTERthe position of the center of the kernel=1 SIGMAsquare root of variance of the cluster=0.1 NORMALIZED would you like the kernel function to be normalized
k: KERNELTransform a set of input coordinates using a kernel function This action is a shortcut and uses the defaults shown here. More details ARGthe arguments that should be used as input to this method=d TYPE the type of kernel to use=gaussian CENTERthe position of the center of the kernel=1 SIGMAsquare root of variance of the cluster=0.1 NORMALIZED would you like the kernel function to be normalized  WEIGHT the weight to multiply this kernel function by=1.0
# PLUMED interprets the command:
# k: KERNEL ARG=d TYPE=gaussian CENTER=1 SIGMA=0.1 NORMALIZED
# as follows (Click the red comment above to revert to the short version of the input):
k_d_refThe CONSTANT action with label k_d_ref calculates the following quantities: Quantity    Type    Description  
k_d_ref scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=1
k_sigmaThe CONSTANT action with label k_sigma calculates the following quantities: Quantity    Type    Description  
k_sigma scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=0.1
k_varThe CUSTOM action with label k_var calculates the following quantities: Quantity    Type    Description  
k_var scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=k_sigma 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
k_icovThe CUSTOM action with label k_icov calculates the following quantities: Quantity    Type    Description  
k_icov scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=k_var FUNCthe function you wish to evaluate=1/x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
k_dist_2The MATRIX_PRODUCT_DIAGONAL action with label k_dist_2 calculates the following quantities: Quantity    Type    Description  
k_dist_2 scalar a vector containing the diagonal elements of the matrix that obtaned by multiplying the two input matrices together: NORMALIZED_EUCLIDEAN_DISTANCECalculate the normalised euclidean distance between two points in CV space More details SQUARED The squared distance should be calculated ARG1The poin that we are calculating the distance from=d ARG2The point that we are calculating the distance to=k_d_ref METRICThe inverse covariance matrix that should be used when calculating the distance=k_icov
k_detThe CUSTOM action with label k_det calculates the following quantities: Quantity    Type    Description  
k_det scalar an arbitrary function: PRODUCTCalculate the product of the input quantities More details ARGThe set of scalars that you would like to multiply together=k_var
k_volThe CUSTOM action with label k_vol calculates the following quantities: Quantity    Type    Description  
k_vol scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=k_det FUNCthe function you wish to evaluate=(sqrt(x)*2.50663) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
kThe CUSTOM action with label k calculates the following quantities: Quantity    Type    Description  
k scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=k_dist_2,k_vol FUNCthe function you wish to evaluate=1.0*exp(-x/2)/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input ---

If your Kernel is a function of two arguments you can use the NORMALIZED_EUCLIDEAN_DISTANCE to evaluate the distance as is done in the following example:

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

d1The DISTANCE action with label d1 calculates the following quantities: Quantity    Type    Description  
d1 scalar the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,2
d2The DISTANCE action with label d2 calculates the following quantities: Quantity    Type    Description  
d2 scalar the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=3,4
kThe KERNEL action with label k calculates the following quantities: Quantity    Type    Description  
k scalar the value of the kernel evaluated at the argument values: KERNELTransform a set of input coordinates using a kernel function This action is a shortcut and it has hidden defaults. More details ARGthe arguments that should be used as input to this method=d1,d2 TYPE the type of kernel to use=gaussian CENTERthe position of the center of the kernel=1,1 SIGMAsquare root of variance of the cluster=0.1,0.1
k: KERNELTransform a set of input coordinates using a kernel function This action is a shortcut and uses the defaults shown here. More details ARGthe arguments that should be used as input to this method=d1,d2 TYPE the type of kernel to use=gaussian CENTERthe position of the center of the kernel=1,1 SIGMAsquare root of variance of the cluster=0.1,0.1  WEIGHT the weight to multiply this kernel function by=1.0
# PLUMED interprets the command:
# k: KERNEL ARG=d1,d2 TYPE=gaussian CENTER=1,1 SIGMA=0.1,0.1
# as follows (Click the red comment above to revert to the short version of the input):
k_d1_refThe CONSTANT action with label k_d1_ref calculates the following quantities: Quantity    Type    Description  
k_d1_ref scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=1
k_d2_refThe CONSTANT action with label k_d2_ref calculates the following quantities: Quantity    Type    Description  
k_d2_ref scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=1
k_sigmaThe CONSTANT action with label k_sigma calculates the following quantities: Quantity    Type    Description  
k_sigma vector the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=0.1,0.1
k_varThe CUSTOM action with label k_var calculates the following quantities: Quantity    Type    Description  
k_var 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=k_sigma 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
k_icovThe CUSTOM action with label k_icov calculates the following quantities: Quantity    Type    Description  
k_icov 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=k_var FUNCthe function you wish to evaluate=1/x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
k_dist_2The MATRIX_PRODUCT_DIAGONAL action with label k_dist_2 calculates the following quantities: Quantity    Type    Description  
k_dist_2 scalar a vector containing the diagonal elements of the matrix that obtaned by multiplying the two input matrices together: NORMALIZED_EUCLIDEAN_DISTANCECalculate the normalised euclidean distance between two points in CV space More details SQUARED The squared distance should be calculated ARG1The poin that we are calculating the distance from=d1,d2 ARG2The point that we are calculating the distance to=k_d1_ref,k_d2_ref METRICThe inverse covariance matrix that should be used when calculating the distance=k_icov
kThe CUSTOM action with label k calculates the following quantities: Quantity    Type    Description  
k scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=k_dist_2 FUNCthe function you wish to evaluate=1.0*exp(-x/2) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input ---

or you can use the MAHALANOBIS_DISTANCE as is done here:

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

phiThe TORSION action with label phi calculates the following quantities: Quantity    Type    Description  
phi scalar the TORSION involving these atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMSthe four atoms involved in the torsional angle=1,2,3,4
psiThe TORSION action with label psi calculates the following quantities: Quantity    Type    Description  
psi scalar the TORSION involving these atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMSthe four atoms involved in the torsional angle=5,6,7,8
kThe KERNEL action with label k calculates the following quantities: Quantity    Type    Description  
k scalar the value of the kernel evaluated at the argument values: KERNELTransform a set of input coordinates using a kernel function This action is a shortcut and it has hidden defaults. More details ...
   ARGthe arguments that should be used as input to this method=phi,psi TYPE the type of kernel to use=von-misses
   CENTERthe position of the center of the kernel=-1.09648066E+0000,-7.17867907E-0001
   COVARthe covariance of the kernel=1.40523052E-0001,-1.05385552E-0001,-1.05385552E-0001,1.63290557E-0001
...
k: KERNELTransform a set of input coordinates using a kernel function This action is a shortcut and uses the defaults shown here. More details ...
   ARGthe arguments that should be used as input to this method=phi,psi TYPE the type of kernel to use=von-misses
   CENTERthe position of the center of the kernel=-1.09648066E+0000,-7.17867907E-0001
   COVARthe covariance of the kernel=1.40523052E-0001,-1.05385552E-0001,-1.05385552E-0001,1.63290557E-0001
 WEIGHT the weight to multiply this kernel function by=1.0
...
# PLUMED interprets the command:
# k: KERNEL ...
#    ARG=phi,psi TYPE=von-misses
#    CENTER=-1.09648066E+0000,-7.17867907E-0001
#    COVAR=1.40523052E-0001,-1.05385552E-0001,-1.05385552E-0001,1.63290557E-0001
# ...
# as follows (Click the red comment above to revert to the short version of the input):
k_phi_refThe CONSTANT action with label k_phi_ref calculates the following quantities: Quantity    Type    Description  
k_phi_ref scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=-1.09648066E+0000
k_psi_refThe CONSTANT action with label k_psi_ref calculates the following quantities: Quantity    Type    Description  
k_psi_ref scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=-7.17867907E-0001
k_covThe CONSTANT action with label k_cov calculates the following quantities: Quantity    Type    Description  
k_cov matrix the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details NCOLS the number of columns in your matrix=2 NROWS the number of rows in your input matrix=2 VALUESthe numbers that are in your constant value=1.40523052E-0001,-1.05385552E-0001,-1.05385552E-0001,1.63290557E-0001
k_icovThe INVERT_MATRIX action with label k_icov calculates the following quantities: Quantity    Type    Description  
k_icov matrix the inverse of the input matrix: INVERT_MATRIXCalculate the inverse of the input matrix More details ARGthe input matrix=k_cov
k_dist_2The COMBINE action with label k_dist_2 calculates the following quantities: Quantity    Type    Description  
k_dist_2 scalar a linear combination: MAHALANOBIS_DISTANCECalculate the Mahalanobis distance between two points in CV space More details SQUARED The squared distance should be calculated ARG1The point that we are calculating the distance from=phi,psi ARG2The point that we are calculating the distance to=k_phi_ref,k_psi_ref METRICThe inverse covariance matrix that should be used when calculating the distance=k_icov  VON_MISSES Compute the mahalanobis distance in a way that is more sympathetic to the periodic boundary conditions
kThe CUSTOM action with label k calculates the following quantities: Quantity    Type    Description  
k scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=k_dist_2 FUNCthe function you wish to evaluate=1.0*exp(-x/2) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input ---

To switch to using the MAHALANOBIS_DISTANCE you use COVAR instead of SIGMA and specify the covariance matrix of the kernel. The metric that is used when evaluating the distance is the inverse of the input covariance matrix.

Notice that you specify the Kernel function in a separate PLUMED input file by using an input like the one shown below:

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

#SETTINGS INPUTFILES=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
phiThe TORSION action with label phi calculates the following quantities: Quantity    Type    Description  
phi scalar the TORSION involving these atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMSthe four atoms involved in the torsional angle=1,2,3,4
psiThe TORSION action with label psi calculates the following quantities: Quantity    Type    Description  
psi scalar the TORSION involving these atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMSthe four atoms involved in the torsional angle=5,6,7,8
kThe KERNEL action with label k calculates the following quantities: Quantity    Type    Description  
k scalar the value of the kernel evaluated at the argument values: KERNELTransform a set of input coordinates using a kernel function This action is a shortcut and it has hidden defaults. More details ARGthe arguments that should be used as input to this method=phi,psi REFERENCEthe file from which to read the kernel parameters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
      8.38235835E-0003      1.34746362E+0000     -2.92912242E+0000      1.50601708E-0001     -1.16056708E-0001     -1.16056708E-0001      2.58187042E-0001  
      1.34976025E-0001     -1.12488647E+0000      2.46856186E+0000      6.47837871E-0002     -5.48993853E-0002     -5.48993853E-0002      1.28240303E-0001  
      2.62404899E-0002      9.93277439E-0001      6.63990207E-0001      3.77594608E-0002     -2.13908228E-0002     -2.13908228E-0002      7.02294006E-0002  
      3.61412967E-0003      9.92586372E-0001     -2.28743740E+0000      6.13474371E-0002      9.32283874E-0003      9.32283874E-0003      4.90062255E-0002  
  
 NUMBER if there are multiple sets of kernel parameters in the input file which set of kernel parameters would you like to read in here=3
k: KERNELTransform a set of input coordinates using a kernel function This action is a shortcut and uses the defaults shown here. More details ARGthe arguments that should be used as input to this method=phi,psi REFERENCEthe file from which to read the kernel parameters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
      8.38235835E-0003      1.34746362E+0000     -2.92912242E+0000      1.50601708E-0001     -1.16056708E-0001     -1.16056708E-0001      2.58187042E-0001  
      1.34976025E-0001     -1.12488647E+0000      2.46856186E+0000      6.47837871E-0002     -5.48993853E-0002     -5.48993853E-0002      1.28240303E-0001  
      2.62404899E-0002      9.93277439E-0001      6.63990207E-0001      3.77594608E-0002     -2.13908228E-0002     -2.13908228E-0002      7.02294006E-0002  
      3.61412967E-0003      9.92586372E-0001     -2.28743740E+0000      6.13474371E-0002      9.32283874E-0003      9.32283874E-0003      4.90062255E-0002  
  
 NUMBER if there are multiple sets of kernel parameters in the input file which set of kernel parameters would you like to read in here=3  TYPE the type of kernel to use=gaussian WEIGHT the weight to multiply this kernel function by=1.0
# PLUMED interprets the command:
# k: KERNEL ARG=phi,psi REFERENCE=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp NUMBER=3
# as follows (Click the red comment above to revert to the short version of the input):
k_phi_refThe CONSTANT action with label k_phi_ref calculates the following quantities: Quantity    Type    Description  
k_phi_ref scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=-1.09648066E+0000
k_psi_refThe CONSTANT action with label k_psi_ref calculates the following quantities: Quantity    Type    Description  
k_psi_ref scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=-7.17867907E-0001
k_covThe CONSTANT action with label k_cov calculates the following quantities: Quantity    Type    Description  
k_cov matrix the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details NCOLS the number of columns in your matrix=2 NROWS the number of rows in your input matrix=2 VALUESthe numbers that are in your constant value=1.40523052E-0001,-1.05385552E-0001,-1.05385552E-0001,1.63290557E-0001
k_icovThe INVERT_MATRIX action with label k_icov calculates the following quantities: Quantity    Type    Description  
k_icov matrix the inverse of the input matrix: INVERT_MATRIXCalculate the inverse of the input matrix More details ARGthe input matrix=k_cov
k_dist_2The MATRIX_PRODUCT_DIAGONAL action with label k_dist_2 calculates the following quantities: Quantity    Type    Description  
k_dist_2 scalar a vector containing the diagonal elements of the matrix that obtaned by multiplying the two input matrices together: MAHALANOBIS_DISTANCECalculate the Mahalanobis distance between two points in CV space More details SQUARED The squared distance should be calculated ARG1The point that we are calculating the distance from=phi,psi ARG2The point that we are calculating the distance to=k_phi_ref,k_psi_ref METRICThe inverse covariance matrix that should be used when calculating the distance=k_icov 
kThe CUSTOM action with label k calculates the following quantities: Quantity    Type    Description  
k scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=k_dist_2 FUNCthe function you wish to evaluate=1.0*exp(-x/2) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input ---

This command computes the same Kernel that was computed in the previous input. The keyword REFERENCE specifies that the parameters are to be read from the file and the keyword NUMBER indicates that the parameters are found on the third line of that file.

Lastly, note that you can use vectors in the input to this shortcut as shown here:

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

#SETTINGS INPUTFILES=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
phiThe TORSION action with label phi calculates the following quantities: Quantity    Type    Description  
phi vector the TORSION for each set of specified atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMS1the four atoms involved in the torsional angle=1,2,3,4 ATOMS2the four atoms involved in the torsional angle=9,10,11,12 ATOMS3the four atoms involved in the torsional angle=17,18,19,20
psiThe TORSION action with label psi calculates the following quantities: Quantity    Type    Description  
psi vector the TORSION for each set of specified atoms: TORSIONCalculate one or multiple torsional angles. More details ATOMS1the four atoms involved in the torsional angle=5,6,7,8 ATOMS2the four atoms involved in the torsional angle=13,14,15,16 ATOMS3the four atoms involved in the torsional angle=21,22,23,24
kThe KERNEL action with label k calculates the following quantities: Quantity    Type    Description  
k vector the value of the kernel evaluated at the argument values: KERNELTransform a set of input coordinates using a kernel function This action is a shortcut and it has hidden defaults. More details ARGthe arguments that should be used as input to this method=phi,psi REFERENCEthe file from which to read the kernel parameters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
      8.38235835E-0003      1.34746362E+0000     -2.92912242E+0000      1.50601708E-0001     -1.16056708E-0001     -1.16056708E-0001      2.58187042E-0001  
      1.34976025E-0001     -1.12488647E+0000      2.46856186E+0000      6.47837871E-0002     -5.48993853E-0002     -5.48993853E-0002      1.28240303E-0001  
      2.62404899E-0002      9.93277439E-0001      6.63990207E-0001      3.77594608E-0002     -2.13908228E-0002     -2.13908228E-0002      7.02294006E-0002  
      3.61412967E-0003      9.92586372E-0001     -2.28743740E+0000      6.13474371E-0002      9.32283874E-0003      9.32283874E-0003      4.90062255E-0002  
  
 NUMBER if there are multiple sets of kernel parameters in the input file which set of kernel parameters would you like to read in here=3
k: KERNELTransform a set of input coordinates using a kernel function This action is a shortcut and uses the defaults shown here. More details ARGthe arguments that should be used as input to this method=phi,psi REFERENCEthe file from which to read the kernel parameters=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp Click here to see an extract from this file.
    ×  FILE: regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp
    #! FIELDS height phi psi sigma_phi_phi sigma_phi_psi sigma_psi_phi sigma_psi_psi 
#! SET kerneltype von-misses
      2.97197455E-0001     -1.91983118E+0000      2.25029540E+0000      2.45960237E-0001     -1.30615381E-0001     -1.30615381E-0001      2.40239117E-0001  
      2.29131448E-0002      1.39809354E+0000      9.54585380E-0002      9.61755708E-0002     -3.55657919E-0002     -3.55657919E-0002      1.06147253E-0001  
      5.06676398E-0001     -1.09648066E+0000     -7.17867907E-0001      1.40523052E-0001     -1.05385552E-0001     -1.05385552E-0001      1.63290557E-0001  
      8.38235835E-0003      1.34746362E+0000     -2.92912242E+0000      1.50601708E-0001     -1.16056708E-0001     -1.16056708E-0001      2.58187042E-0001  
      1.34976025E-0001     -1.12488647E+0000      2.46856186E+0000      6.47837871E-0002     -5.48993853E-0002     -5.48993853E-0002      1.28240303E-0001  
      2.62404899E-0002      9.93277439E-0001      6.63990207E-0001      3.77594608E-0002     -2.13908228E-0002     -2.13908228E-0002      7.02294006E-0002  
      3.61412967E-0003      9.92586372E-0001     -2.28743740E+0000      6.13474371E-0002      9.32283874E-0003      9.32283874E-0003      4.90062255E-0002  
  
 NUMBER if there are multiple sets of kernel parameters in the input file which set of kernel parameters would you like to read in here=3  TYPE the type of kernel to use=gaussian WEIGHT the weight to multiply this kernel function by=1.0
# PLUMED interprets the command:
# k: KERNEL ARG=phi,psi REFERENCE=regtest/pamm/rt-pamm-periodic/2D-testc-0.75.pammp NUMBER=3
# as follows (Click the red comment above to revert to the short version of the input):
k_phi_refThe CONSTANT action with label k_phi_ref calculates the following quantities: Quantity    Type    Description  
k_phi_ref scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=-1.09648066E+0000
k_psi_refThe CONSTANT action with label k_psi_ref calculates the following quantities: Quantity    Type    Description  
k_psi_ref scalar the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details VALUESthe numbers that are in your constant value=-7.17867907E-0001
k_covThe CONSTANT action with label k_cov calculates the following quantities: Quantity    Type    Description  
k_cov matrix the constant value that was read from the plumed input: CONSTANTCreate a constant value that can be passed to actions More details NCOLS the number of columns in your matrix=2 NROWS the number of rows in your input matrix=2 VALUESthe numbers that are in your constant value=1.40523052E-0001,-1.05385552E-0001,-1.05385552E-0001,1.63290557E-0001
k_icovThe INVERT_MATRIX action with label k_icov calculates the following quantities: Quantity    Type    Description  
k_icov matrix the inverse of the input matrix: INVERT_MATRIXCalculate the inverse of the input matrix More details ARGthe input matrix=k_cov
k_dist_2The MATRIX_PRODUCT_DIAGONAL action with label k_dist_2 calculates the following quantities: Quantity    Type    Description  
k_dist_2 vector a vector containing the diagonal elements of the matrix that obtaned by multiplying the two input matrices together: MAHALANOBIS_DISTANCECalculate the Mahalanobis distance between two points in CV space More details SQUARED The squared distance should be calculated ARG1The point that we are calculating the distance from=phi,psi ARG2The point that we are calculating the distance to=k_phi_ref,k_psi_ref METRICThe inverse covariance matrix that should be used when calculating the distance=k_icov 
kThe CUSTOM action with label k calculates the following quantities: Quantity    Type    Description  
k 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=k_dist_2 FUNCthe function you wish to evaluate=1.0*exp(-x/2) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input ---

The output k here is a vector with three components. The first component is the kernel evaluated with the torsion involving atoms 1, 2, 3 and 4 and the torsion involving atoms 5, 6, 7 and 8. The second component is the kernel evaluated with the torsion involving atoms 9, 10, 11 and 12 and the torsion involving atoms 13, 14, 15 and 16. The third component is the kernel evaluated with the torsion involving atoms 17, 18, 19 and 20 and the torsion involving atoms 21, 22, 23 and 24.

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	the arguments that should be used as input to this method

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 arguments that should be used as input to this method
TYPE	compulsory	gaussian	the type of kernel to use
CENTER	compulsory	none	the position of the center of the kernel
COVAR	compulsory	none	the covariance of the kernel
WEIGHT	compulsory	1.0	the weight to multiply this kernel function by
NUMBER	compulsory	1	if there are multiple sets of kernel parameters in the input file which set of kernel parameters would you like to read in here
SIGMA	optional	not used	square root of variance of the cluster
REFERENCE	optional	not used	the file from which to read the kernel parameters
NORMALIZED	optional	false	would you like the kernel function to be normalized