Action: MARGINAL

Module	gridtools
Description	Usage
Compute a marginal from the input multi-dimensional function
output value	type
the function evaluated onto the interpolated grid	grid

Details and examples

Compute a marginal from the input multi-dimensional function

The marginals of the function $f(x,y)$ are defined as:

$$g(y) = \int f(x,y) \textrm{d}x \qquad \textrm{and} \qquad h(x) = \int f(x,y) \textrm{d}y$$

This action takes a function of two or more coordinates that is stored on a grid in input. The marginal of the input function is then computed via numerical integration. To see how this works in practice consider the following input:

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.x
vector
the x-component of the vector connecting the two atoms
d1.y
vector
the y-component of the vector connecting the two atoms
d1.z
vector
the z-component of the vector connecting the two atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMS1the pair of atom that we are calculating the distance between=1,3 ATOMS2the pair of atom that we are calculating the distance between=1,4 ATOMS3the pair of atom that we are calculating the distance between=1,5 ATOMS4the pair of atom that we are calculating the distance between=1,6 COMPONENTS calculate the x, y and z components of the distance separately and store them as label

kThe KDE action with label k calculates the following quantities:
 Quantity   
 Type   
 Description  
k
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=d1.x,d1.y BANDWIDTHthe bandwidths for kernel density esimtation=0.02,0.02 KERNEL the kernel function you are using=gaussian GRID_BINthe number of bins for the grid=50,50 GRID_MIN the lower bounds for the grid=0,0 GRID_MAX the upper bounds for the grid=1,1
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=k FILE the file on which to write the grid=func_xy.grid STRIDE the frequency with which the grid should be output to the file=1
The DUMPGRID action with label  calculates somethingm1The MARGINAL action with label m1 calculates the following quantities:
 Quantity   
 Type   
 Description  
m1
grid
the function evaluated onto the interpolated grid: MARGINALCompute a marginal from the input multi-dimensional function More details ARGthe label for function on the grid that you would like to interpolate=k DIRthe direction along which the marginal is being computed=1
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=m1 FILE the file on which to write the grid=func_x.grid STRIDE the frequency with which the grid should be output to the file=1
m2The MARGINAL action with label m2 calculates the following quantities:
 Quantity   
 Type   
 Description  
m2
grid
the function evaluated onto the interpolated grid: MARGINALCompute a marginal from the input multi-dimensional function More details ARGthe label for function on the grid that you would like to interpolate=k DIRthe direction along which the marginal is being computed=2
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=m1 FILE the file on which to write the grid=func_y.grid STRIDE the frequency with which the grid should be output to the file=1

This input uses the KDE action to compute a distribution from the x and y components of the distances that were computed using the DISTANCE command. We then output this two dimensional histogram and use the MARGINAL command to compute the distributions for the x and y components of the vector separately.

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
DIR	compulsory	none	the direction along which the marginal is being computed
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.