CUSTOM
This is part of the function module

Calculate a combination of variables using a custom expression.

This action computes an arbitrary function of one or more collective variables. Arguments are chosen with the ARG keyword, and the function is provided with the FUNC string. Notice that this string should contain no space. Within FUNC, one can refer to the arguments as x,y,z, and t (up to four variables provided as ARG). This names can be customized using the VAR keyword (see examples below).

This function is implemented using the Lepton library, that allows to evaluate algebraic expressions and to automatically differentiate them.

If you want a function that depends not only on collective variables but also on time you can use the TIME action.

Examples

The following input tells plumed to perform a metadynamics using as a CV the difference between two distances.

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tested on master





 (see also DISTANCE, COMBINE, and METAD). Notice that forces applied to diff will be correctly propagated to atoms 10, 12, and 15. Also notice that since CUSTOM is used without the VAR option the two arguments should be referred to as x and y in the expression FUNC. For simple functions such as this one it is possible to use COMBINE.


The following input tells plumed to print the angle between vectors identified by atoms 1,2 and atoms 2,3 its square (as computed from the x,y,z components) and the distance again as computed from the square root of the square. 


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


tested on master







 (See also PRINT and DISTANCE).


Notice that this action implements a large number of functions (trigonometric, exp, log, etc). Among the useful functions, have a look at the step function (that is the Heaviside function). step(x) is defined as 1 when x is positive and 0 when x is negative. This allows for a straightforward implementation of if clauses.


For example, imagine that you want to implement a restraint that only acts when a distance is larger than 0.5. You can do it with 


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tested on master







 (see also DISTANCE, PRINT, and RESTRAINT)


The meaning of the function 0.5*step(0.5-x)+x*step(x-0.5) is:
    

  • If x<0.5 (step(0.5-x)!=0) use 0.5
    • 

  • If x>0.5 (step(x-0.5)!=0) use x Notice that the same could have been obtained using an UPPER_WALLS However, with CUSTOM you can create way more complex definitions.
    • 



Warning
If you apply forces on the variable (as in the previous example) you should make sure that the variable is continuous! Conversely, if you are just analyzing a trajectory you can safely use discontinuous variables.


A possible continuity check with gnuplot is 
# this allow to step function to be used in gnuplot:
gnuplot> step(x)=0.5*(erf(x*10000000)+1)
# here you can test your function
gnuplot> p 0.5*step(0.5-x)+x*step(x-0.5)

Also notice that you can easily make logical operations on the conditions that you create. The equivalent of the AND operator is the product: step(1.0-x)*step(x-0.5) is only equal to 1 when x is between 0.5 and 1.0. By combining negation and AND you can obtain an OR. That is, 1-step(1.0-x)*step(x-0.5) is only equal to 1 when x is outside the 0.5-1.0 interval.


CUSTOM can be used in combination with DISTANCE to implement variants of the DISTANCE keyword that were present in PLUMED 1.3 and that allowed to compute the distance of a point from a line defined by two other points, or the progression along that line. 


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


tested on master