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.

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

dAB: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. 
=10,12 The DISTANCE action with label dAB calculates a single scalar value
dAC: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. 
=10,15 The DISTANCE action with label dAC calculates a single scalar value
diff: CUSTOM ARGthe input for this action is the scalar output from one or more other actions. 
=dAB,dAC FUNCcompulsory keyword 
the function you wish to evaluate 
=y-x PERIODICcompulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The CUSTOM action with label diff calculates a single scalar value
# notice: the previous line could be replaced with the following
# diff: COMBINE ARG=dAB,dAC COEFFICIENTS=-1,1
METAD ARGthe input for this action is the scalar output from one or more other actions. 
=diff SIGMAcompulsory keyword 
the widths of the Gaussian hills 
=0.1 HEIGHTthe heights of the Gaussian hills. 
=0.5 BIASFACTORuse well tempered metadynamics and use this bias factor. 
=10 PACEcompulsory keyword 
the frequency for hill addition 
=100 The METAD action with label

(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

d1: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. 
=1,2 COMPONENTS( default=off ) calculate the x, y and z components of the distance separately and
store them as label.x, 
 The DISTANCE action with label d1 calculates the following quantities:

 Quantity    Description  
d1.x the x-component of the vector connecting the two atoms
d1.y the y-component of the vector connecting the two atoms
d1.z the z-component of the vector connecting the two atoms


d2: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. 
=2,3 COMPONENTS( default=off ) calculate the x, y and z components of the distance separately and
store them as label.x, 
 The DISTANCE action with label d2 calculates the following quantities:

 Quantity    Description  
d2.x the x-component of the vector connecting the two atoms
d2.y the y-component of the vector connecting the two atoms
d2.z the z-component of the vector connecting the two atoms


theta: CUSTOM ...
   
   ARGthe input for this action is the scalar output from one or more other actions. 
=d1.x,d1.y,d1.z,d2.x,d2.y,d2.z 
   VARthe names to give each of the arguments in the function. =ax,ay,az,bx,by,bz 
   FUNCcompulsory keyword 
the function you wish to evaluate =acos((ax*bx+ay*by+az*bz)/sqrt((ax*ax+ay*ay+az*az)*(bx*bx+by*by+bz*bz))) 
   PERIODICcompulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. =NO 
...The CUSTOM action with label theta calculates a single scalar value
PRINT ARGthe input for this action is the scalar output from one or more other actions. 
=theta The PRINT action with label

(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

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

d: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. 
=10,15 The DISTANCE action with label d calculates a single scalar value
m: CUSTOM ARGthe input for this action is the scalar output from one or more other actions. 
=d FUNCcompulsory keyword 
the function you wish to evaluate 
=0.5*step(0.5-x)+x*step(x-0.5) PERIODICcompulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The CUSTOM action with label m calculates a single scalar value
# check the function you are applying:
PRINT ARGthe input for this action is the scalar output from one or more other actions. 
=d,m FILEthe name of the file on which to output these quantities 
=checkme The PRINT action with label 
RESTRAINT ARGthe input for this action is the scalar output from one or more other actions. 
=d ATcompulsory keyword 
the position of the restraint 
=0.5 KAPPAcompulsory keyword ( default=0.0 )
specifies that the restraint is harmonic and what the values of the force constants
on each of the variables are 
=10.0 The RESTRAINT action with label

(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

# take center of atoms 1 to 10 as reference point 1
p1: CENTER ATOMSthe list of atoms which are involved the virtual atom's definition. 
=1-10 The CENTER action with label p1 calculates the position of a virtual atom
# take center of atoms 11 to 20 as reference point 2
p2: CENTER ATOMSthe list of atoms which are involved the virtual atom's definition. 
=11-20 The CENTER action with label p2 calculates the position of a virtual atom
# take center of atoms 21 to 30 as reference point 3
p3: CENTER ATOMSthe list of atoms which are involved the virtual atom's definition. 
=21-30 The CENTER action with label p3 calculates the position of a virtual atom
# compute distances
d12: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. 
=p1,p2 The DISTANCE action with label d12 calculates a single scalar value
d13: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. 
=p1,p3 The DISTANCE action with label d13 calculates a single scalar value
d23: DISTANCE ATOMSthe pair of atom that we are calculating the distance between. 
=p2,p3 The DISTANCE action with label d23 calculates a single scalar value
# compute progress variable of the projection of point p3
# along the vector joining p1 and p2
# notice that progress is measured from the middle point
onaxis: CUSTOM ARGthe input for this action is the scalar output from one or more other actions. 
=d13,d23,d12 FUNCcompulsory keyword 
the function you wish to evaluate 
=(0.5*(y^2-x^2)/z) PERIODICcompulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The CUSTOM action with label onaxis calculates a single scalar value
# compute between point p3 and the vector joining p1 and p2
fromaxis: CUSTOM ARGthe input for this action is the scalar output from one or more other actions. 
=d13,d23,d12,onaxis VARthe names to give each of the arguments in the function. 
=x,y,z,o FUNCcompulsory keyword 
the function you wish to evaluate 
=(0.5*(y^2+x^2)-o^2-0.25*z^2) PERIODICcompulsory keyword 
if the output of your function is periodic then you should specify the periodicity
of the function. 
=NO The CUSTOM action with label fromaxis calculates a single scalar value

PRINT ARG=onaxis,fromaxis

Notice that these equations have been used to combine RMSD from different snapshots of a protein so as to define progression (S) and distance (Z) variables [98].

Glossary of keywords and components

Compulsory keywords

PERIODIC	if the output of your function is periodic then you should specify the periodicity of the function. If the output is not periodic you must state this using PERIODIC=NO
FUNC	the function you wish to evaluate

Options

NUMERICAL_DERIVATIVES

( default=off ) calculate the derivatives for these quantities numerically

ARG

the input for this action is the scalar output from one or more other actions. The particular scalars that you will use are referenced using the label of the action. If the label appears on its own then it is assumed that the Action calculates a single scalar value. The value of this scalar is thus used as the input to this new action. If * or *.* appears the scalars calculated by all the proceeding actions in the input file are taken. Some actions have multi-component outputs and each component of the output has a specific label. For example a DISTANCE action labelled dist may have three components x, y and z. To take just the x component you should use dist.x, if you wish to take all three components then use dist.*.More information on the referencing of Actions can be found in the section of the manual on the PLUMED Getting Started. Scalar values can also be referenced using POSIX regular expressions as detailed in the section on Regular Expressions. To use this feature you you must compile PLUMED with the appropriate flag. You can use multiple instances of this keyword i.e. ARG1, ARG2, ARG3...

VAR

the names to give each of the arguments in the function. If you have up to three arguments in your function you can use x, y and z to refer to them. Otherwise you must use this flag to give your variables names.

Quantity	Description
d1.x	the x-component of the vector connecting the two atoms
d1.y	the y-component of the vector connecting the two atoms
d1.z	the z-component of the vector connecting the two atoms

Quantity	Description
d2.x	the x-component of the vector connecting the two atoms
d2.y	the y-component of the vector connecting the two atoms
d2.z	the z-component of the vector connecting the two atoms