Shortcut: MOMENTS

Module	function
Description	Usage
Calculate central moments from the distribution of input quantities

Input

The arguments that serve as the input for this action are specified using one or more of the keywords in the following table.

Further details and examples

Calculate central moments from the distribution of input quantities

This action takes a set of $N$ input arguments, $s_i$, and evaluates the $k$th central moment of the distribution of input arguments using:

$$\mu_k = \frac{1}{N} \sum_{i=1}^N ( s_i - \langle s \rangle )^k \qquad \textrm{where} \qquad \langle s \rangle = \frac{1}{N} \sum_{i=1}^N s_i$$

A single moments action can evaluate more than one central moment at once so, for example, the input below can be used to calculate the second and third central moment for the distribution of the four input distances.

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

d12The DISTANCE action with label d12 calculates the following quantities:
 Quantity   
 Type   
 Description  
d12
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
d13The DISTANCE action with label d13 calculates the following quantities:
 Quantity   
 Type   
 Description  
d13
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=1,3
d14The DISTANCE action with label d14 calculates the following quantities:
 Quantity   
 Type   
 Description  
d14
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=1,4
d15The DISTANCE action with label d15 calculates the following quantities:
 Quantity   
 Type   
 Description  
d15
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=1,5
mvThe MOMENTS action with label mv calculates the following quantities:
 Quantity   
 Type   
 Description  
mv.moment-2
scalar
the central moments of the distribution of values. The second central moment would be referenced elsewhere in the input file using label.moment-2, the third as label.moment-3, etc.  This is the 2th of these quantities
mv.moment-3
scalar
the central moments of the distribution of values. The second central moment would be referenced elsewhere in the input file using label.moment-2, the third as label.moment-3, etc.  This is the 3th of these quantities: MOMENTSCalculate central moments from the distribution of input quantities More details ARGthe values input to this function=d12,d13,d14,d15 POWERScalculate the central moments of the distribution of collective variables=2,3
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=mv.moment-2,mv.moment-3 FILEthe name of the file on which to output these quantities=colvar

Notice that you can also achieve the same result using the following input:

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

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=1,3 ATOMS3the pair of atom that we are calculating the distance between=1,4 ATOMS4the pair of atom that we are calculating the distance between=1,5
mvThe MOMENTS action with label mv calculates the following quantities:
 Quantity   
 Type   
 Description  
mv.moment-2
scalar
the central moments of the distribution of values. The second central moment would be referenced elsewhere in the input file using label.moment-2, the third as label.moment-3, etc.  This is the 2th of these quantities
mv.moment-3
scalar
the central moments of the distribution of values. The second central moment would be referenced elsewhere in the input file using label.moment-2, the third as label.moment-3, etc.  This is the 3th of these quantities: MOMENTSCalculate central moments from the distribution of input quantities More details ARGthe values input to this function=d POWERScalculate the central moments of the distribution of collective variables=2,3
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=mv.moment-2,mv.moment-3 FILEthe name of the file on which to output these quantities=colvar

In this second case the four distances are passed to the MOMENTS action as a vector. The MOMENTS action then outputs 2 components - the two central moments that were requested.

These examples are representative the only two ways you can use this action. In input it can accept either a list of scalars or a single vector. It does not accept matrices or a list of vectors in input.

Syntax

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