Shortcut: GRADIENT

Module	gridtools
Description	Usage
Calculate the gradient of an input grid
output value	type
the desired gradient	scalar

Details and examples

Calculate the gradient of an input grid

This shortcut implements the gradient CV that was used to drive nucleation and that is described in the paper cited below. A description that explains how this CV is evaluated and used can be found in the paper.

An example input for computing and printing the gradient CV that is discussed in the paper is shown below:

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

s1xyzThe GRADIENT action with label s1xyz calculates the following quantities: Quantity    Type    Description  
s1xyz scalar the desired gradient: GRADIENTCalculate the gradient of an input grid This action is a shortcut and it has hidden defaults. More details ATOMScalculate the gradient of these atoms=1-50 ORIGINwe will use the position of this atom as the origin in our calculation=1 DIR the directions in which we are calculating the graident=xyz NBINSnumber of bins to use in each direction for the calculation of the gradient=4 SIGMAthe width of the function to be used for kernel density estimation=1.0
s1xyz: GRADIENTCalculate the gradient of an input grid This action is a shortcut and uses the defaults shown here. More details ATOMScalculate the gradient of these atoms=1-50 ORIGINwe will use the position of this atom as the origin in our calculation=1 DIR the directions in which we are calculating the graident=xyz NBINSnumber of bins to use in each direction for the calculation of the gradient=4 SIGMAthe width of the function to be used for kernel density estimation=1.0  KERNEL the type of kernel function to be used in the grids=gaussian-bin
# PLUMED interprets the command:
# s1xyz: GRADIENT ATOMS=1-50 ORIGIN=1 DIR=xyz NBINS=4 SIGMA=1.0
# as follows (Click the red comment above to revert to the short version of the input):
s1xyz_distThe DISTANCE action with label s1xyz_dist calculates the following quantities: Quantity    Type    Description  
s1xyz_dist.x vector the x-component of the vector connecting the two atoms
s1xyz_dist.y vector the y-component of the vector connecting the two atoms
s1xyz_dist.z vector the z-component of the vector connecting the two atoms: DISTANCESCalculate the distances between multiple piars of atoms More details ORIGINcalculate the distance of all the atoms specified using the ATOMS keyword from this point=1 ATOMSthe pairs of atoms that you would like to calculate the angles for=1-50 COMPONENTS calculate the x, y and z components of the distance separately and store them as label
s1xyz_xhistoThe KDE action with label s1xyz_xhisto calculates the following quantities: Quantity    Type    Description  
s1xyz_xhisto grid a function on a grid that was obtained by doing a Kernel Density Estimation using the input arguments: KDECreate a histogram from the input scalar/vector/matrix using KDE More details ARGthe label for the value that should be used to construct the histogram=s1xyz_dist.x GRID_BINthe number of bins for the grid=4 KERNEL the kernel function you are using=gaussian-bin BANDWIDTHthe bandwidths for kernel density esimtation=1.0
s1xyz_xgrad_shiftThe INTERPOLATE_GRID action with label s1xyz_xgrad_shift calculates the following quantities: Quantity    Type    Description  
s1xyz_xgrad_shift grid the function evaluated onto the interpolated grid: INTERPOLATE_GRIDInterpolate a smooth function stored on a grid onto a grid with a smaller grid spacing. More details ARGthe label for function on the grid that you would like to interpolate=s1xyz_xhisto INTERPOLATION_TYPE the method to use for interpolation=ceiling GRID_BINthe number of bins for the grid=4
s1xyz_xgrad_x2The CUSTOM action with label s1xyz_xgrad_x2 calculates the following quantities: Quantity    Type    Description  
s1xyz_xgrad_x2 grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=s1xyz_xhisto,s1xyz_xgrad_shift FUNCthe function you wish to evaluate=(x-y)*(x-y) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s1xyz_xgradThe SUM action with label s1xyz_xgrad calculates the following quantities: Quantity    Type    Description  
s1xyz_xgrad 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=s1xyz_xgrad_x2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s1xyz_yhistoThe KDE action with label s1xyz_yhisto calculates the following quantities: Quantity    Type    Description  
s1xyz_yhisto grid a function on a grid that was obtained by doing a Kernel Density Estimation using the input arguments: KDECreate a histogram from the input scalar/vector/matrix using KDE More details ARGthe label for the value that should be used to construct the histogram=s1xyz_dist.y GRID_BINthe number of bins for the grid=4 KERNEL the kernel function you are using=gaussian-bin BANDWIDTHthe bandwidths for kernel density esimtation=1.0
s1xyz_ygrad_shiftThe INTERPOLATE_GRID action with label s1xyz_ygrad_shift calculates the following quantities: Quantity    Type    Description  
s1xyz_ygrad_shift grid the function evaluated onto the interpolated grid: INTERPOLATE_GRIDInterpolate a smooth function stored on a grid onto a grid with a smaller grid spacing. More details ARGthe label for function on the grid that you would like to interpolate=s1xyz_yhisto INTERPOLATION_TYPE the method to use for interpolation=ceiling GRID_BINthe number of bins for the grid=4
s1xyz_ygrad_x2The CUSTOM action with label s1xyz_ygrad_x2 calculates the following quantities: Quantity    Type    Description  
s1xyz_ygrad_x2 grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=s1xyz_yhisto,s1xyz_ygrad_shift FUNCthe function you wish to evaluate=(x-y)*(x-y) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s1xyz_ygradThe SUM action with label s1xyz_ygrad calculates the following quantities: Quantity    Type    Description  
s1xyz_ygrad 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=s1xyz_ygrad_x2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s1xyz_zhistoThe KDE action with label s1xyz_zhisto calculates the following quantities: Quantity    Type    Description  
s1xyz_zhisto grid a function on a grid that was obtained by doing a Kernel Density Estimation using the input arguments: KDECreate a histogram from the input scalar/vector/matrix using KDE More details ARGthe label for the value that should be used to construct the histogram=s1xyz_dist.z GRID_BINthe number of bins for the grid=4 KERNEL the kernel function you are using=gaussian-bin BANDWIDTHthe bandwidths for kernel density esimtation=1.0
s1xyz_zgrad_shiftThe INTERPOLATE_GRID action with label s1xyz_zgrad_shift calculates the following quantities: Quantity    Type    Description  
s1xyz_zgrad_shift grid the function evaluated onto the interpolated grid: INTERPOLATE_GRIDInterpolate a smooth function stored on a grid onto a grid with a smaller grid spacing. More details ARGthe label for function on the grid that you would like to interpolate=s1xyz_zhisto INTERPOLATION_TYPE the method to use for interpolation=ceiling GRID_BINthe number of bins for the grid=4
s1xyz_zgrad_x2The CUSTOM action with label s1xyz_zgrad_x2 calculates the following quantities: Quantity    Type    Description  
s1xyz_zgrad_x2 grid the grid obtained by doing an element-wise application of an arbitrary function to the input grid: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=s1xyz_zhisto,s1xyz_zgrad_shift FUNCthe function you wish to evaluate=(x-y)*(x-y) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s1xyz_zgradThe SUM action with label s1xyz_zgrad calculates the following quantities: Quantity    Type    Description  
s1xyz_zgrad 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=s1xyz_zgrad_x2 PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
s1xyzThe COMBINE action with label s1xyz calculates the following quantities: Quantity    Type    Description  
s1xyz scalar a linear combination: COMBINECalculate a polynomial combination of a set of other variables. More details ARGthe values input to this function=s1xyz_xgrad,s1xyz_ygrad,s1xyz_zgrad 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=s1xyz FILEthe name of the file on which to output these quantities=colvar

Full list of keywords

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

Keyword	Type	Default	Description
ORIGIN	compulsory	none	we will use the position of this atom as the origin in our calculation
NBINS	compulsory	none	number of bins to use in each direction for the calculation of the gradient
DIR	compulsory	xyz	the directions in which we are calculating the graident
SIGMA	compulsory	none	the width of the function to be used for kernel density estimation
KERNEL	compulsory	gaussian-bin	the type of kernel function to be used in the grids
ATOMS	compulsory	none	calculate the gradient of these atoms

References

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

F. Giberti, G. A. Tribello, M. Parrinello, Transient Polymorphism in NaCl. Journal of Chemical Theory and Computation. 9, 2526–2530 (2013)

Quantity	Type	Description
s1xyz	scalar	the desired gradient