Action: INTERPOLATE_GRID

Module	gridtools
Description	Usage
Interpolate a smooth function stored on a grid onto a grid with a smaller grid spacing.
output value	type
the function evaluated onto the interpolated grid	grid

Details and examples

Interpolate a smooth function stored on a grid onto a grid with a smaller grid spacing.

This action takes a function evaluated on a grid as input and can be used to interpolate the values of that function on to a finer grained grid. By default the interpolation within this algorithm is done using splines.

Examples

The input below can be used to post process a trajectory. It calculates a HISTOGRAM as a function the distance between atoms 1 and 2 using kernel density estimation. During the calculation the values of the kernels are evaluated at 100 points on a uniform grid between 0.0 and 3.0. Prior to outputting this function at the end of the simulation this function is interpolated onto a finer grid of 200 points between 0.0 and 3.0.

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

xThe DISTANCE action with label x calculates the following quantities: Quantity    Type    Description  
x 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
hA1The HISTOGRAM action with label hA1 calculates the following quantities: Quantity    Type    Description  
hA1 grid the estimate of the histogram as a function of the argument that was obtained: HISTOGRAMAccumulate the average probability density along a few CVs from a trajectory. This action is a shortcut and it has hidden defaults. More details ARGthe quantities that are being used to construct the histogram=x GRID_MIN the lower bounds for the grid=0.0 GRID_MAX the upper bounds for the grid=3.0 GRID_BINthe number of bins for the grid=100 BANDWIDTHthe bandwidths for kernel density esimtation=0.1
hA1: HISTOGRAMAccumulate the average probability density along a few CVs from a trajectory. This action is a shortcut and uses the defaults shown here. More details ARGthe quantities that are being used to construct the histogram=x GRID_MIN the lower bounds for the grid=0.0 GRID_MAX the upper bounds for the grid=3.0 GRID_BINthe number of bins for the grid=100 BANDWIDTHthe bandwidths for kernel density esimtation=0.1  NORMALIZATION This controls how the data is normalized it can be set equal to true, false or ndata=ndata STRIDE the frequency with which to store data for averaging=1 CLEAR the frequency with whihc to clear the data that is being averaged=0
# PLUMED interprets the command:
# hA1: HISTOGRAM ARG=x GRID_MIN=0.0 GRID_MAX=3.0 GRID_BIN=100 BANDWIDTH=0.1
# as follows (Click the red comment above to revert to the short version of the input):
hA1_weightThe CONSTANT action with label hA1_weight calculates the following quantities: Quantity    Type    Description  
hA1_weight scalar 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=1
hA1_kdeThe KDE action with label hA1_kde calculates the following quantities: Quantity    Type    Description  
hA1_kde 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=x  BANDWIDTHthe bandwidths for kernel density esimtation=0.1 GRID_BINthe number of bins for the grid=100 GRID_MAX the upper bounds for the grid=3.0 GRID_MIN the lower bounds for the grid=0.0
hA1_kdepThe CUSTOM action with label hA1_kdep calculates the following quantities: Quantity    Type    Description  
hA1_kdep 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=hA1_kde,hA1_weight 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
hA1_uThe ACCUMULATE action with label hA1_u calculates the following quantities: Quantity    Type    Description  
hA1_u grid a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory More details ARGthe label of the argument that is being added to on each timestep=hA1_kdep STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0 
hA1_nsumThe ACCUMULATE action with label hA1_nsum calculates the following quantities: Quantity    Type    Description  
hA1_nsum scalar a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory More details ARGthe label of the argument that is being added to on each timestep=hA1_weight STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0 
hA1The CUSTOM action with label hA1 calculates the following quantities: Quantity    Type    Description  
hA1 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=hA1_u,hA1_nsum 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 --- iiThe INTERPOLATE_GRID action with label ii calculates the following quantities: Quantity    Type    Description  
ii 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. This action has hidden defaults. More details ARGthe label for function on the grid that you would like to interpolate=hA1 GRID_BINthe number of bins for the grid=200
ii: INTERPOLATE_GRIDInterpolate a smooth function stored on a grid onto a grid with a smaller grid spacing. This action uses the defaults shown here. More details ARGthe label for function on the grid that you would like to interpolate=hA1 GRID_BINthe number of bins for the grid=200  GRID_MIN the lower bounds for the grid=auto GRID_MAX the upper bounds for the grid=auto INTERPOLATION_TYPE the method to use for interpolation=spline
DUMPGRIDOutput the function on the grid to a file with the PLUMED grid format. More details ARGthe label for the grid that you would like to output=ii FILE the file on which to write the grid=histo.dat

When specifying the parameters of the interpolating grid you can use GRID_BIN to specify the number of grid points or GRID_SPACING to specify the spacing between grid points as shown below:

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

xThe DISTANCE action with label x calculates the following quantities: Quantity    Type    Description  
x 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
hA1The HISTOGRAM action with label hA1 calculates the following quantities: Quantity    Type    Description  
hA1 grid the estimate of the histogram as a function of the argument that was obtained: HISTOGRAMAccumulate the average probability density along a few CVs from a trajectory. This action is a shortcut and it has hidden defaults. More details ARGthe quantities that are being used to construct the histogram=x GRID_MIN the lower bounds for the grid=0.0 GRID_MAX the upper bounds for the grid=3.0 GRID_BINthe number of bins for the grid=100 BANDWIDTHthe bandwidths for kernel density esimtation=0.1
hA1: HISTOGRAMAccumulate the average probability density along a few CVs from a trajectory. This action is a shortcut and uses the defaults shown here. More details ARGthe quantities that are being used to construct the histogram=x GRID_MIN the lower bounds for the grid=0.0 GRID_MAX the upper bounds for the grid=3.0 GRID_BINthe number of bins for the grid=100 BANDWIDTHthe bandwidths for kernel density esimtation=0.1  NORMALIZATION This controls how the data is normalized it can be set equal to true, false or ndata=ndata STRIDE the frequency with which to store data for averaging=1 CLEAR the frequency with whihc to clear the data that is being averaged=0
# PLUMED interprets the command:
# hA1: HISTOGRAM ARG=x GRID_MIN=0.0 GRID_MAX=3.0 GRID_BIN=100 BANDWIDTH=0.1
# as follows (Click the red comment above to revert to the short version of the input):
hA1_weightThe CONSTANT action with label hA1_weight calculates the following quantities: Quantity    Type    Description  
hA1_weight scalar 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=1
hA1_kdeThe KDE action with label hA1_kde calculates the following quantities: Quantity    Type    Description  
hA1_kde 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=x  BANDWIDTHthe bandwidths for kernel density esimtation=0.1 GRID_BINthe number of bins for the grid=100 GRID_MAX the upper bounds for the grid=3.0 GRID_MIN the lower bounds for the grid=0.0
hA1_kdepThe CUSTOM action with label hA1_kdep calculates the following quantities: Quantity    Type    Description  
hA1_kdep 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=hA1_kde,hA1_weight 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
hA1_uThe ACCUMULATE action with label hA1_u calculates the following quantities: Quantity    Type    Description  
hA1_u grid a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory More details ARGthe label of the argument that is being added to on each timestep=hA1_kdep STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0 
hA1_nsumThe ACCUMULATE action with label hA1_nsum calculates the following quantities: Quantity    Type    Description  
hA1_nsum scalar a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory More details ARGthe label of the argument that is being added to on each timestep=hA1_weight STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0 
hA1The CUSTOM action with label hA1 calculates the following quantities: Quantity    Type    Description  
hA1 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=hA1_u,hA1_nsum 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 --- iiThe INTERPOLATE_GRID action with label ii calculates the following quantities: Quantity    Type    Description  
ii 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. This action has hidden defaults. More details ARGthe label for function on the grid that you would like to interpolate=hA1 GRID_SPACINGthe approximate grid spacing (to be used as an alternative or together with GRID_BIN)=0.05 INTERPOLATION_TYPE the method to use for interpolation=floor
ii: INTERPOLATE_GRIDInterpolate a smooth function stored on a grid onto a grid with a smaller grid spacing. This action uses the defaults shown here. More details ARGthe label for function on the grid that you would like to interpolate=hA1 GRID_SPACINGthe approximate grid spacing (to be used as an alternative or together with GRID_BIN)=0.05 INTERPOLATION_TYPE the method to use for interpolation=floor  GRID_MIN the lower bounds for the grid=auto GRID_MAX the upper bounds for the grid=auto
DUMPGRIDOutput the function on the grid to a file with the PLUMED grid format. More details ARGthe label for the grid that you would like to output=ii FILE the file on which to write the grid=histo.dat

In the above input spline interpolation is not used. Instead, if you evaluating the function at value $x$ , which is $x_n < x < x_{n+1}$ where $x_n$ and $x_{n+1}$ are two points where the values for the function on the input grid are $f(x_n)$ and $f(x_{n+1})$ then $f(x)=f(x_n)$ . If you want $f(x)=f(x_{n+1})$ you use INTERPOLATION_TYPE=ceiling. Alternatively, you can use linear interpolation as has been done in the following input.

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

xThe DISTANCE action with label x calculates the following quantities: Quantity    Type    Description  
x 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
hA1The HISTOGRAM action with label hA1 calculates the following quantities: Quantity    Type    Description  
hA1 grid the estimate of the histogram as a function of the argument that was obtained: HISTOGRAMAccumulate the average probability density along a few CVs from a trajectory. This action is a shortcut and it has hidden defaults. More details ARGthe quantities that are being used to construct the histogram=x GRID_MIN the lower bounds for the grid=0.0 GRID_MAX the upper bounds for the grid=3.0 GRID_BINthe number of bins for the grid=100 BANDWIDTHthe bandwidths for kernel density esimtation=0.1
hA1: HISTOGRAMAccumulate the average probability density along a few CVs from a trajectory. This action is a shortcut and uses the defaults shown here. More details ARGthe quantities that are being used to construct the histogram=x GRID_MIN the lower bounds for the grid=0.0 GRID_MAX the upper bounds for the grid=3.0 GRID_BINthe number of bins for the grid=100 BANDWIDTHthe bandwidths for kernel density esimtation=0.1  NORMALIZATION This controls how the data is normalized it can be set equal to true, false or ndata=ndata STRIDE the frequency with which to store data for averaging=1 CLEAR the frequency with whihc to clear the data that is being averaged=0
# PLUMED interprets the command:
# hA1: HISTOGRAM ARG=x GRID_MIN=0.0 GRID_MAX=3.0 GRID_BIN=100 BANDWIDTH=0.1
# as follows (Click the red comment above to revert to the short version of the input):
hA1_weightThe CONSTANT action with label hA1_weight calculates the following quantities: Quantity    Type    Description  
hA1_weight scalar 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=1
hA1_kdeThe KDE action with label hA1_kde calculates the following quantities: Quantity    Type    Description  
hA1_kde 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=x  BANDWIDTHthe bandwidths for kernel density esimtation=0.1 GRID_BINthe number of bins for the grid=100 GRID_MAX the upper bounds for the grid=3.0 GRID_MIN the lower bounds for the grid=0.0
hA1_kdepThe CUSTOM action with label hA1_kdep calculates the following quantities: Quantity    Type    Description  
hA1_kdep 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=hA1_kde,hA1_weight 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
hA1_uThe ACCUMULATE action with label hA1_u calculates the following quantities: Quantity    Type    Description  
hA1_u grid a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory More details ARGthe label of the argument that is being added to on each timestep=hA1_kdep STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0 
hA1_nsumThe ACCUMULATE action with label hA1_nsum calculates the following quantities: Quantity    Type    Description  
hA1_nsum scalar a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory More details ARGthe label of the argument that is being added to on each timestep=hA1_weight STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0 
hA1The CUSTOM action with label hA1 calculates the following quantities: Quantity    Type    Description  
hA1 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=hA1_u,hA1_nsum 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 --- iiThe INTERPOLATE_GRID action with label ii calculates the following quantities: Quantity    Type    Description  
ii 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=hA1 GRID_MIN the lower bounds for the grid=0.015 GRID_MAX the upper bounds for the grid=2.985 GRID_BINthe number of bins for the grid=99 INTERPOLATION_TYPE the method to use for interpolation=linear
DUMPGRIDOutput the function on the grid to a file with the PLUMED grid format. More details ARGthe label for the grid that you would like to output=ii FILE the file on which to write the grid=histo.dat

Notice that the way we have specified GRID_MIN, GRID_MAX and GRID_BIN in the above input ensures that function is evaluated at the $n-1$ mid points that lie between the points on the input grid.

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	grid	the label for function on the grid that you would like to interpolate

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 label for function on the grid that you would like to interpolate
GRID_MIN	compulsory	auto	the lower bounds for the grid
GRID_MAX	compulsory	auto	the upper bounds for the grid
INTERPOLATION_TYPE	compulsory	spline	the method to use for interpolation
GRID_BIN	optional	not used	the number of bins for the grid
GRID_SPACING	optional	not used	the approximate grid spacing (to be used as an alternative or together with GRID_BIN)
SERIAL	optional	false	do the calculation in serial. Further information about this flag can be found here.
USEGPU	optional	false	run this calculation on the GPU. Further information about this flag can be found here.

Quantity	Type	Description
x	scalar	the DISTANCE between this pair of atoms