Action: FIND_GRID_MAXIMUM

Module	gridtools
Description	Usage
Find the point with the highest value of the function on the grid

Details and examples

Find the point with the highest value of the function on the grid

This command takes a function on a grid as input and returns multiple scalars. One of the returned scalars (the one with component optval) is the value of the input function at its highest point. The other scalars returned are the coordinates for which the function takes this particular value.

As the input grid has the values of the function evaluated over a grid of points we find this maximum value by finding the point on the grid where the function has its lowest value using interpolation and conjugate gradients. The coordinates of the grid point where the function's value is highest will be used as an initial coordinate for the optimisation. We then interpolate the function to find the optimum. You can use use the CGTOL keyword to control the conjugate gradient algorithm that is used to find the location of the maximum in the interpolated function.

To print out the location on the grid where the function is maximised and the value of the function at that point you can use an input like the one 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 --- maxThe FIND_GRID_MAXIMUM action with label max calculates the following quantities: Quantity    Type    Description  
max.x_opt scalar the values of the arguments of the function at the optimum can be referenced elsewhere in the input file by using the names of the arguments followed by the string _opt This particular component measures this quantity for the input CV named x
max.optval scalar the value of the function at the optimum: FIND_GRID_MAXIMUMFind the point with the highest value of the function on the grid This action has hidden defaults. More details ARGthe label for the function on the grid that you would like to find the optimum in=hA1
max: FIND_GRID_MAXIMUMFind the point with the highest value of the function on the grid This action uses the defaults shown here. More details ARGthe label for the function on the grid that you would like to find the optimum in=hA1  CGTOL the tolerance for the conjugate gradient optimization=1E-4
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=max.x_opt,max.optval STRIDE the frequency with which the quantities of interest should be output=0

Notice that we set STRIDE=0 in the PRINT command here so the position of the maximum is only output once at the end of the simulation.

If for any reason you do not want to use interpolation and conjugate gradient to find the optimum you can use the NOINTERPOL flag 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 --- maxThe FIND_GRID_MAXIMUM action with label max calculates the following quantities: Quantity    Type    Description  
max.x_opt scalar the values of the arguments of the function at the optimum can be referenced elsewhere in the input file by using the names of the arguments followed by the string _opt This particular component measures this quantity for the input CV named x
max.optval scalar the value of the function at the optimum: FIND_GRID_MAXIMUMFind the point with the highest value of the function on the grid More details ARGthe label for the function on the grid that you would like to find the optimum in=hA1 NOINTERPOL do not interpolate the function when finding the optimum
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=max.x_opt,max.optval STRIDE the frequency with which the quantities of interest should be output=0

The FIND_GRID_MAXIMUM action then outputs the coordinates of the grid point where the function is largest as well as the value of the function on that grid point.

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 the function on the grid that you would like to find the optimum in

Output components

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

Name	Type	Description
optval	scalar	the value of the function at the optimum
_opt	scalar	the values of the arguments of the function at the optimum can be referenced elsewhere in the input file by using the names of the arguments followed by the string _opt

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 the function on the grid that you would like to find the optimum in
CGTOL	compulsory	1E-4	the tolerance for the conjugate gradient optimization
NOINTERPOL	optional	false	do not interpolate the function when finding the optimum

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