Action: CONDITIONAL_PATH

Module	pathbias
Description	Usage
Evaluate a fixed conditional path log mixture, with its full chain rule.
output value	type
the dimensionless conditional path log mixture	scalar

Details and examples

Evaluate a fixed conditional path log mixture, with its full chain rule.

For positive path score a and positive conditional normalizer m(c), this function returns log R = log[(1-lambda)+lambda*a/m(c)]. ARG must contain exactly three nonperiodic scalars: c, log(a), log(m(c)), in that order. COUPLING is lambda in [0,1). LOWER and UPPER bound the admitted domain of c; evaluation outside this closed interval fails instead of extrapolating.

The derivatives with respect to the three arguments are (0,chi,-chi), where chi=lambdaa/(mR). The explicit c argument only checks the domain. The normalizer argument MUST retain its dependence on c: freezing a fitted function does not mean dropping its derivative. All functions must be fixed during production. This action does not learn m or preserve external file identity across restarts. Verify frozen input/model hashes before restarting.

A bias V=B_c-kBTlog R is built using CUSTOM and BIASVALUE. kBT must be in the same energy units as B_c. With an exact m=E_0[a|c], the selected c marginal of the fixed B_c ensemble is preserved. Approximate m still defines a fixed potential with full-path weight exp(betaV), but does not imply that marginal identity or any efficiency improvement. Every bead in one path shares the same path weight; beads are not independent samples.

The following two-replica example uses a mean Cartesian distance component, then squares it, rather than averaging the squared components. It assumes consistent nonperiodic coordinate images across the replicas. This scalar example does not implement arbitrary molecular Cartesian-centroid CVs.

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

#SETTINGS NREPLICAS=2
dThe DISTANCE action with label d calculates the following quantities:
 Quantity   
 Type   
 Description  
d.x
scalar
the x-component of the vector connecting the two atoms
d.y
scalar
the y-component of the vector connecting the two atoms
d.z
scalar
the z-component of the vector connecting the two atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,2 COMPONENTS calculate the x, y and z components of the distance separately and store them as label NOPBC ignore the periodic boundary conditions when calculating distances
meanThe ENSEMBLE action with label mean calculates the following quantities:
 Quantity   
 Type   
 Description  
mean.d.x
scalar
the average for argument d.x: ENSEMBLECalculates the replica averaging of a collective variable over multiple replicas. More details ARGthe labels of the values from which the function is calculated=d.x
cThe CUSTOM action with label c calculates the following quantities:
 Quantity   
 Type   
 Description  
c
scalar
an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=mean.d.x FUNCthe function you wish to evaluate=x*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
hThe CUSTOM action with label h calculates the following quantities:
 Quantity   
 Type   
 Description  
h
scalar
an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=d.x FUNCthe function you wish to evaluate=exp(-x*x/2) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
fractionThe ENSEMBLE action with label fraction calculates the following quantities:
 Quantity   
 Type   
 Description  
fraction.h
scalar
the average for argument h: ENSEMBLECalculates the replica averaging of a collective variable over multiple replicas. More details ARGthe labels of the values from which the function is calculated=h
logaThe CUSTOM action with label loga calculates the following quantities:
 Quantity   
 Type   
 Description  
loga
scalar
an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=fraction.h FUNCthe function you wish to evaluate=log(0.1+x) PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
logmThe CUSTOM action with label logm calculates the following quantities:
 Quantity   
 Type   
 Description  
logm
scalar
an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=c FUNCthe function you wish to evaluate=-1+0.2*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
ratioThe CONDITIONAL_PATH action with label ratio calculates the following quantities:
 Quantity   
 Type   
 Description  
ratio
scalar
the dimensionless conditional path log mixture: CONDITIONAL_PATHEvaluate a fixed conditional path log mixture, with its full chain rule. More details ARGthe labels of the values from which the function is calculated=c,loga,logm COUPLINGmixture fraction in the half-open interval [0,1)=0.5 LOWERinclusive lower limit of the conditioning argument=0 UPPERinclusive upper limit of the conditioning argument=4
correctionThe CUSTOM action with label correction calculates the following quantities:
 Quantity   
 Type   
 Description  
correction
scalar
an arbitrary function: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=ratio FUNCthe function you wish to evaluate=-2.5*x PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
biasThe BIASVALUE action with label bias calculates the following quantities:
 Quantity   
 Type   
 Description  
bias.bias
scalar
the instantaneous value of the bias potential
bias.correction_bias
scalar
one or multiple instances of this quantity can be referenced elsewhere in the input file. these quantities will named with  the arguments of the bias followed by the character string _bias. These quantities tell the user how much the bias is due to each of the colvars. This particular component measures this quantity for the input CV named correction: BIASVALUETakes the value of one variable and use it as a bias More details ARGthe labels of the scalar/vector arguments whose values will be used as a bias on the system=correction
PRINTPrint quantities to a file. More details ARGthe labels of the values that you would like to print to the file=c,loga,logm,ratio,bias.* FILEthe name of the file on which to output these quantities=COLVAR

The illustrative logm above is not a fitted conditional reference. Supply a qualified frozen normalizer and a separate fixed centroid bias for production. The molecular dynamics adapter must provide consistent dynamical force scaling and single-path energy accounting. This action does not apply additional factors of the bead count.

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	the labels of the values from which the function is calculated

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 labels of the values from which the function is calculated
COUPLING	compulsory	none	mixture fraction in the half-open interval [0,1)
LOWER	compulsory	none	inclusive lower limit of the conditioning argument
UPPER	compulsory	none	inclusive upper limit of the conditioning argument
NUMERICAL_DERIVATIVESThis keyword do not have examples	optional	false	calculate the derivatives for these quantities numerically