Action: ACCUMULATE

Module	generic
Description	Usage
Sum the elements of this value over the course of the trajectory
output value	type
a sum calculated from the time series of the input quantity	scalar/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	scalar/grid	the label of the argument that is being added to on each timestep

Further details and examples

Sum the elements of this value over the course of the trajectory

This action is used to sum the outputs from another action over the course of the trajectory. This is useful if you want to calculate the average value that a CV took over the course of a simulation. As an example, the following input can be used to calculate the average distance between atom 1 and atom 2.

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

cThe CONSTANT action with label c calculates the following quantities: Quantity    Type    Description  
c 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=1
c: 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=1  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 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
# This adds together the value of the distance on every step
sThe ACCUMULATE action with label s calculates the following quantities: Quantity    Type    Description  
s scalar a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory This action has hidden defaults. More details ARGthe label of the argument that is being added to on each timestep=d STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1
s: ACCUMULATESum the elements of this value over the course of the trajectory This action uses the defaults shown here. More details ARGthe label of the argument that is being added to on each timestep=d 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
# This adds one every time we add a new distance to the value s
nThe ACCUMULATE action with label n calculates the following quantities: Quantity    Type    Description  
n scalar a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory This action has hidden defaults. More details ARGthe label of the argument that is being added to on each timestep=c STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1
n: ACCUMULATESum the elements of this value over the course of the trajectory This action uses the defaults shown here. More details ARGthe label of the argument that is being added to on each timestep=c 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
# This is thus the average distance
aThe CUSTOM action with label a calculates the following quantities: Quantity    Type    Description  
a scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=s,n 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
# This prints out the average over the whole trajectory (STRIDE=0 means print at end only)
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=a FILEthe name of the file on which to output these quantities=average.dat STRIDE the frequency with which the quantities of interest should be output=0

You can use this action for block averaging by using the CLEAR keyword as shown below:

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

cThe CONSTANT action with label c calculates the following quantities: Quantity    Type    Description  
c 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=1
c: 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=1  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 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
# This adds together the value of the distance on every step
sThe ACCUMULATE action with label s calculates the following quantities: Quantity    Type    Description  
s 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=d 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=1000
# This adds one every time we add a new distance to the value s
nThe ACCUMULATE action with label n calculates the following quantities: Quantity    Type    Description  
n 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=c 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=1000
# This is thus the average distance
aThe CUSTOM action with label a calculates the following quantities: Quantity    Type    Description  
a scalar an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=s,n 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
# This prints out the average over the whole trajectory (STRIDE=0 means print at end only)
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=a FILEthe name of the file on which to output these quantities=average.dat STRIDE the frequency with which the quantities of interest should be output=1000

The instructions CLEAR=1000 in the above input tells PLUMED to set the values s and n back to zero after 1000 new steps have been performed. The PRINT action will thus print a block average that is taken from the first 1000 steps of the trajectory, a second block average from the second 1000 steps of the trajectory and so on.

Estimating histograms

We can also use this action to construct histograms. The example below shows how you can estimate the distribution of distances between atoms 1 and 2 that are sampled over the course of the trajectory.

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

cThe CONSTANT action with label c calculates the following quantities: Quantity    Type    Description  
c 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=1
c: 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=1  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 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
# Construct the instantaneous histogram from the instantaneous value of the distance
kdeThe KDE action with label kde calculates the following quantities: Quantity    Type    Description  
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 This action has hidden defaults. More details ARGthe label for the value that should be used to construct the histogram=d BANDWIDTHthe bandwidths for kernel density esimtation=0.05 GRID_MIN the lower bounds for the grid=0 GRID_MAX the upper bounds for the grid=5 GRID_BINthe number of bins for the grid=250
kde: KDECreate a histogram from the input scalar/vector/matrix using KDE This action uses the defaults shown here. More details ARGthe label for the value that should be used to construct the histogram=d BANDWIDTHthe bandwidths for kernel density esimtation=0.05 GRID_MIN the lower bounds for the grid=0 GRID_MAX the upper bounds for the grid=5 GRID_BINthe number of bins for the grid=250  KERNEL the kernel function you are using=GAUSSIAN CUTOFF the cutoff at which to stop evaluating the kernel functions is set equal to sqrt(2*x)*bandwidth in each direction where x is this number=6.25
# Now add together all the instantaneous histograms
histThe ACCUMULATE action with label hist calculates the following quantities: Quantity    Type    Description  
hist grid a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory This action has hidden defaults. More details ARGthe label of the argument that is being added to on each timestep=kde STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1
hist: ACCUMULATESum the elements of this value over the course of the trajectory This action uses the defaults shown here. More details ARGthe label of the argument that is being added to on each timestep=kde 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
# And normalise the histogram
nThe ACCUMULATE action with label n calculates the following quantities: Quantity    Type    Description  
n scalar a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory This action has hidden defaults. More details ARGthe label of the argument that is being added to on each timestep=c STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1
n: ACCUMULATESum the elements of this value over the course of the trajectory This action uses the defaults shown here. More details ARGthe label of the argument that is being added to on each timestep=c 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
aThe CUSTOM action with label a calculates the following quantities: Quantity    Type    Description  
a 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=hist,n 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 the final histogram
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=a FILE the file on which to write the grid=histo.grid

At first glance the fact that we use a KDE action to construct an instaneous histogram from a single distance may appear odd. The reason for doing this, however, is to introduce a clear distinction between the syntaxes that are used for spatial and temporal averaging. To see what I mean consider the following input:

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

cThe CONSTANT action with label c calculates the following quantities: Quantity    Type    Description  
c 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=5
c: 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=5  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 ATOMS5the pair of atom that we are calculating the distance between=9,10
# Construct the instantaneous histogram from the instantaneous value of the distance
kdeThe KDE action with label kde calculates the following quantities: Quantity    Type    Description  
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 This action has hidden defaults. More details ARGthe label for the value that should be used to construct the histogram=d BANDWIDTHthe bandwidths for kernel density esimtation=0.05 GRID_MIN the lower bounds for the grid=0 GRID_MAX the upper bounds for the grid=5 GRID_BINthe number of bins for the grid=250
kde: KDECreate a histogram from the input scalar/vector/matrix using KDE This action uses the defaults shown here. More details ARGthe label for the value that should be used to construct the histogram=d BANDWIDTHthe bandwidths for kernel density esimtation=0.05 GRID_MIN the lower bounds for the grid=0 GRID_MAX the upper bounds for the grid=5 GRID_BINthe number of bins for the grid=250  KERNEL the kernel function you are using=GAUSSIAN CUTOFF the cutoff at which to stop evaluating the kernel functions is set equal to sqrt(2*x)*bandwidth in each direction where x is this number=6.25
# Now add together all the instantaneous histograms
histThe ACCUMULATE action with label hist calculates the following quantities: Quantity    Type    Description  
hist grid a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory This action has hidden defaults. More details ARGthe label of the argument that is being added to on each timestep=kde STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1
hist: ACCUMULATESum the elements of this value over the course of the trajectory This action uses the defaults shown here. More details ARGthe label of the argument that is being added to on each timestep=kde 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
# And normalise the histogram
nThe ACCUMULATE action with label n calculates the following quantities: Quantity    Type    Description  
n scalar a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory This action has hidden defaults. More details ARGthe label of the argument that is being added to on each timestep=c STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1
n: ACCUMULATESum the elements of this value over the course of the trajectory This action uses the defaults shown here. More details ARGthe label of the argument that is being added to on each timestep=c 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
aThe CUSTOM action with label a calculates the following quantities: Quantity    Type    Description  
a 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=hist,n 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 the final histogram
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=a FILE the file on which to write the grid=histo.grid

This input computes 5 distances. Kernels correpsonding to all five of these distances are added to the instaneous histogram that is constructed using the KDE action. When we call the accumulate action here we are thus not simply adding a single kernel to the accumulated grid when we add the the elements from kde.

Syntax

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

Keyword	Type	Default	Description
ARG	input	none	the label of the argument that is being added to on each timestep
STRIDE	compulsory	1	the frequency with which the data should be collected and added to the quantity being averaged
CLEAR	compulsory	0	the frequency with which to clear all the accumulated data
NUMERICAL_DERIVATIVES	optional	false	calculate the derivatives for these quantities numerically
UPDATE_FROM	optional	not used	Only update this action from this time
UPDATE_UNTIL	optional	not used	Only update this action until this time

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Quantity	Type	Description
c	scalar	the constant value that was read from the plumed input