Action: SPHERICAL_KDE

Module	gridtools
Description	Usage
Create a histogram from the input scalar/vector/matrix using SPHERICAL_KDE
output value	type
a function on a grid that was obtained by doing a Kernel Density Estimation using the input arguments	grid

Details and examples

Create a histogram from the input scalar/vector/matrix using SPHERICAL_KDE

This action operates similarly to KDE but it is designed to be used for investigating directional statistics. It is particularly useful if you are looking at the distribution of bond vectors as illustrated in the input below:

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

# Calculate all the bond vectors
d1The CONTACT_MATRIX action with label d1 calculates the following quantities:
 Quantity   
 Type   
 Description  
d1.w
matrix
a matrix containing the weights for the bonds between each pair of atoms
d1.x
matrix
the projection of the bond on the x axis
d1.y
matrix
the projection of the bond on the y axis
d1.z
matrix
the projection of the bond on the z axis: CONTACT_MATRIXAdjacency matrix in which two atoms are adjacent if they are within a certain cutoff. More details GROUPspecifies the list of atoms that should be assumed indistinguishable=1-100 SWITCHthe input for the switching function that acts upon the distance between each pair of atoms. Options for this keyword are explained in the documentation for LESS_THAN.={RATIONAL R_0=0.1} COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
# Normalise the bond vectors
magThe CUSTOM action with label mag calculates the following quantities:
 Quantity   
 Type   
 Description  
mag
matrix
the matrix obtained by doing an element-wise application of an arbitrary function to the input matrix: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=d1.x,d1.y,d1.z FUNCthe function you wish to evaluate=sqrt(x*x+y*y+z*z) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
d1xThe CUSTOM action with label d1x calculates the following quantities:
 Quantity   
 Type   
 Description  
d1x
matrix
the matrix obtained by doing an element-wise application of an arbitrary function to the input matrix: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=d1.x,mag 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
d1yThe CUSTOM action with label d1y calculates the following quantities:
 Quantity   
 Type   
 Description  
d1y
matrix
the matrix obtained by doing an element-wise application of an arbitrary function to the input matrix: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=d1.y,mag 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
d1zThe CUSTOM action with label d1z calculates the following quantities:
 Quantity   
 Type   
 Description  
d1z
matrix
the matrix obtained by doing an element-wise application of an arbitrary function to the input matrix: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=d1.z,mag 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 construct the KDE
kdeThe SPHERICAL_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: SPHERICAL_KDECreate a histogram from the input scalar/vector/matrix using SPHERICAL_KDE More details ARGthe label for the value that should be used to construct the histogram=d1x,d1y,d1z HEIGHTS this keyword takes the label of an action that calculates a vector of values=d1.w CONCENTRATIONthe concentration parameter for the Von Mises-Fisher distributions=100 GRID_BINthe number of points on the fibonacci sphere at which the density should be evaluated=144

Each bond vector here contributes a Fisher von-Mises kernel to the spherical grid. This spherical grid is constructed using a Fibonnacci sphere algorithm so the number of specified using the GRID_BIN keyword must be a Fibonacci number.

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/vector/matrix	the label for the value that should be used to construct the histogram

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 value that should be used to construct the histogram
CONCENTRATION	compulsory	none	the concentration parameter for the Von Mises-Fisher distributions
HEIGHTS	compulsory	1.0	this keyword takes the label of an action that calculates a vector of values
GRID_BIN	compulsory	none	the number of points on the fibonacci sphere at which the density should be evaluated
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.