Action: TD_CUSTOM

Module	ves
Description	Usage
Target distribution given by an arbitrary mathematical expression (static or dynamic).

Details and examples

Target distribution given by an arbitrary mathematical expression (static or dynamic).

Use as a target distribution the distribution defined by

$$p(\mathbf{s}) = \frac{f(\mathbf{s})}{\int d\mathbf{s} \, f(\mathbf{s})}$$

where $f(\mathbf{s})$ is some arbitrary mathematical function that is parsed by the lepton library.

The function $f(\mathbf{s})$ is given by the FUNCTION keywords by using s1,s2,..., as variables for the arguments $\mathbf{s}=(s_1,s_2,\ldots,s_d)$. If one variable is not given the target distribution will be taken as uniform in that argument.

It is also possible to include the free energy surface $F(\mathbf{s})$ in the target distribution by using the FE variable. In this case the target distribution is dynamic and needs to be updated with current best estimate of $F(\mathbf{s})$, similarly as for the TD_WELLTEMPERED "well-tempered target distribution". Furthermore, the inverse temperature $\beta = (k_{\mathrm{B}}T)^{-1}$ and the thermal energy $k_{\mathrm{B}}T$ can be included by using the beta and $k_B T$ variables.

The target distribution will be automatically normalized over the region on which it is defined on. Therefore, the function given in FUNCTION needs to be non-negative and it must be possible to normalize the function. The code will perform checks to make sure that this is indeed the case.

Examples

Here we use as shifted Maxwell-Boltzmann distribution as a target distribution in one-dimension. Note that it is not need to include the normalization factor as the distribution will be automatically normalized.

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

TD_CUSTOMTarget distribution given by an arbitrary mathematical expression (static or dynamic). More details ...
 FUNCTIONThe function you wish to use for the target distribution where you should use the variables _s1_,_s2_,=(s1+20)^2*exp(-(s1+20)^2/(2*10.0^2))
 LABELa label for the action so that its output can be referenced in the input to other actions=td
... TD_CUSTOM
The TD_CUSTOM action with label td calculates something

Here we have a two dimensional target distribution where we use a generalized normal distribution for argument $s_2$ while the distribution for $s_1$ is taken as uniform as the variable s1 is not included in the function.

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

TD_CUSTOMTarget distribution given by an arbitrary mathematical expression (static or dynamic). More details ...
 FUNCTIONThe function you wish to use for the target distribution where you should use the variables _s1_,_s2_,=exp(-(abs(s2-20.0)/5.0)^4.0)
 LABELa label for the action so that its output can be referenced in the input to other actions=td
... TD_CUSTOM
The TD_CUSTOM action with label td calculates something

By using the FE variable the target distribution can depend on the free energy surface $F(\mathbf{s})$. For example, the following input is identical to using TD_WELLTEMPERED with a bias factor of 10.

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

TD_CUSTOMTarget distribution given by an arbitrary mathematical expression (static or dynamic). More details ...
 FUNCTIONThe function you wish to use for the target distribution where you should use the variables _s1_,_s2_,=exp(-(beta/10.0)*FE)
 LABELa label for the action so that its output can be referenced in the input to other actions=td
... TD_CUSTOM
The TD_CUSTOM action with label td calculates something

Here the inverse temperature is automatically obtained by using the beta variable. It is also possible to use the $k_B T$ variable. The following syntax will give the exact same results as the syntax above

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

TD_CUSTOMTarget distribution given by an arbitrary mathematical expression (static or dynamic). More details ...
 FUNCTIONThe function you wish to use for the target distribution where you should use the variables _s1_,_s2_,=exp(-(1.0/(kBT*10.0))*FE)
 LABELa label for the action so that its output can be referenced in the input to other actions=td
... TD_CUSTOM
The TD_CUSTOM action with label td calculates something

Full list of keywords

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

Keyword	Type	Default	Description
FUNCTION	compulsory	none	The function you wish to use for the target distribution where you should use the variables s1,s2,
WELLTEMPERED_FACTORThis keyword do not have examples	optional	not used	Broaden the target distribution such that it is taken as [p(s)]^(1/gamma) where gamma is the well tempered factor given here
SHIFT_TO_ZEROThis keyword do not have examples	optional	false	Shift the minimum value of the target distribution to zero