Shortcut: CYLINDRICAL_HARMONIC

Module	symfunc
Description	Usage
Calculate the cylindrical harmonic function

Details and examples

Calculate the cylindrical harmonic function

This action allows you to the value of the following complex function. The action outputs two components that are the real and imaginary parts of the following function:

$$z = w (\frac{x}{r} + \frac{y}{r} i )^n \qquad \textrm{where} \qquad r = \sqrt(x^2 + y^2}$$

In this expression $n$ is a parameter that is specified using the DEGREE keyword. $x$ and $y$ are the input arguments and $w$ is an optional input weight, which is set equal to one if only two arguments are provided in input. At present, the arguments for this action must be matrices. These arguments must all have the same shape as the two output components will also be matrices that are calculated by applying the function above to each of the elements of the input matrix in turn.

The following intput provides an example that demonstrates how this function is used:

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

dThe DISTANCE_MATRIX action with label d calculates the following quantities:
 Quantity   
 Type   
 Description  
d.w
matrix
a matrix containing the weights for the bonds between each pair of atoms
d.x
matrix
the projection of the bond on the x axis
d.y
matrix
the projection of the bond on the y axis
d.z
matrix
the projection of the bond on the z axis: DISTANCE_MATRIXCalculate a matrix of distances between atoms. This action has hidden defaults. More details GROUPthe atoms for which you would like to calculate the adjacency matrix=1-10 COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
d: DISTANCE_MATRIXCalculate a matrix of distances between atoms. This action uses the defaults shown here. More details GROUPthe atoms for which you would like to calculate the adjacency matrix=1-10 COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix  NL_CUTOFF The cutoff for the neighbor list=0.0 NL_STRIDE The frequency with which we are updating the atoms in the neighbor list=1 CUTOFF ignore distances that have a value larger than this cutoff=-1
cThe CYLINDRICAL_HARMONIC action with label c calculates the following quantities:
 Quantity   
 Type   
 Description  
c.rm
matrix
the real part of the cylindrical harmonic
c.im
matrix
the imaginary part of the cylindrical harmonic: CYLINDRICAL_HARMONICCalculate the cylindrical harmonic function More details DEGREEthe value of the n parameter in the equation above=6 ARGthe values input to this function=d.x,d.y
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c.rm FILEthe name of the file on which to output these quantities=real_part
The PRINT action with label  calculates somethingPRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c.im FILEthe name of the file on which to output these quantities=imaginary_part

The DISTANCE_MATRIX command in the above input computes 3 $10\times10$ matrices. Two of these $10\times10$ matrices are used in the input to the cylindrical harmonic command, which in turn outputs two $10\times10$ matrices that contain the real and imaginary parts when the function above is applied element-wise to the above input. These two $10\times10$ matrices are then output to two separate files.

In the above example the weights for every distance is set equal to one. The following example shows how an argument can be used to set the $w$ values to use when computing the function above.

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

sThe CONTACT_MATRIX action with label s calculates the following quantities:
 Quantity   
 Type   
 Description  
s
matrix
a matrix containing the weights for the bonds between each pair of atoms: 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=1-10 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=1.0}
scThe CONTACT_MATRIX action with label sc calculates the following quantities:
 Quantity   
 Type   
 Description  
sc.w
matrix
a matrix containing the weights for the bonds between each pair of atoms
sc.x
matrix
the projection of the bond on the x axis
sc.y
matrix
the projection of the bond on the y axis
sc.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=1-10 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=1.0} COMPONENTS also calculate the components of the vector connecting the atoms in the contact matrix
cThe CYLINDRICAL_HARMONIC action with label c calculates the following quantities:
 Quantity   
 Type   
 Description  
c.rm
matrix
the real part of the cylindrical harmonic
c.im
matrix
the imaginary part of the cylindrical harmonic: CYLINDRICAL_HARMONICCalculate the cylindrical harmonic function More details DEGREEthe value of the n parameter in the equation above=6 ARGthe values input to this function=sc.x,sc.y,s
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c.rm FILEthe name of the file on which to output these quantities=real_part
The PRINT action with label  calculates somethingPRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c.im FILEthe name of the file on which to output these quantities=imaginary_part

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 values input to this function

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
rm	matrix	the real part of the cylindrical harmonic
im	matrix	the imaginary part of the cylindrical harmonic

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 values input to this function
DEGREE	compulsory	none	the value of the n parameter in the equation above