TD_LINEAR_COMBINATION

	This is part of the ves module
	It is only available if you configure PLUMED with ./configure –enable-modules=ves . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list.

Target distribution given by linear combination of distributions (static or dynamic).

Employ a target distribution that is a linear combination of the other distributions, defined as

\[ p(\mathbf{s}) = \sum_{i} w_{i} \, p_{i}(\mathbf{s}) \]

where the weights \(w_{i}\) are normalized to 1, \(\sum_{i}w_{i}=1\).

The labels of the distributions \(p_{i}(\mathbf{s})\) to be used in the linear combination are given in the DISTRIBUTIONS keyword.

The weights \(w_{i}\) can be given using the WEIGHTS keyword. The distributions are weighted equally if no weights are given.

It is assumed that all the distributions \(p_{i}(\mathbf{s})\) are normalized. If that is not the case for some reason should you normalize each distribution separately by using the NORMALIZE keyword when defining them in the input file (i.e. before the TD_LINEAR_COMBINATION action). Note that normalizing the overall linear combination will generally lead to different results than normalizing each distribution separately.

The linear combination will be a dynamic target distribution if one or more of the distributions used is a dynamic distribution, otherwise it will be a static distribution.

Examples

Here we employ a linear combination of a uniform and a Gaussian distribution. No weights are given so the two distributions will be weighted equally.

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

td_uni: TD_UNIFORM The TD_UNIFORM action with label td_uni
td_gauss: TD_GAUSSIAN 
CENTER1
The centers of the Gaussian distributions. 
=-2.0 
SIGMA1
The standard deviations of the Gaussian distributions. 
=0.5 The TD_GAUSSIAN action with label td_gauss
td_comb: TD_LINEAR_COMBINATION 
DISTRIBUTIONS
compulsory keyword 
The labels of the target distribution actions to be used in the linear combination.
=td_uni,td_gauss The TD_LINEAR_COMBINATION action with label td_comb

Here we employ a linear combination of a uniform and two Gaussian distribution. The weights are automatically normalized to 1 such that giving WEIGHTS=1.0,1.0,2.0 as we do here is equal to giving WEIGHTS=0.25,0.25,0.50.

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

td_uni: TD_UNIFORM The TD_UNIFORM action with label td_uni
td_gauss1: TD_GAUSSIAN 
CENTER1
The centers of the Gaussian distributions. 
=-2.0,-2.0 
SIGMA1
The standard deviations of the Gaussian distributions. 
=0.5,0.3 The TD_GAUSSIAN action with label td_gauss1
td_gauss2: TD_GAUSSIAN 
CENTER1
The centers of the Gaussian distributions. 
=+2.0,+2.0 
SIGMA1
The standard deviations of the Gaussian distributions. 
=0.3,0.5 The TD_GAUSSIAN action with label td_gauss2
td_comb: TD_LINEAR_COMBINATION ...
   
DISTRIBUTIONS
compulsory keyword 
The labels of the target distribution actions to be used in the linear combination.
=td_uni,td_gauss1,td_gauss2 
   
WEIGHTS
The weights of target distributions. 
=1.0,1.0,2.0 
   
...The TD_LINEAR_COMBINATION action with label td_comb

In the above example the two Gaussian kernels are given using two separate DISTRIBUTION keywords. As the TD_GAUSSIAN target distribution allows multiple centers is it also possible to use just one DISTRIBUTION keyword for the two Gaussian kernels. This is shown in the following example which will give the exact same result as the one above as the weights have been appropriately adjusted

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

td_uni: TD_UNIFORM The TD_UNIFORM action with label td_uni
td_gauss: TD_GAUSSIAN ...
   
CENTER1
The centers of the Gaussian distributions. 
=-2.0,-2.0 
SIGMA1
The standard deviations of the Gaussian distributions. 
=0.5,0.3 
   
CENTER2
The centers of the Gaussian distributions. 
=+2.0,+2.0 
SIGMA2
The standard deviations of the Gaussian distributions. 
=0.3,0.5 
   
WEIGHTS
The weights of the Gaussian distributions. 
=1.0,2.0 
   
...The TD_GAUSSIAN action with label td_gauss
td_comb: TD_LINEAR_COMBINATION ...
   
DISTRIBUTIONS
compulsory keyword 
The labels of the target distribution actions to be used in the linear combination.
=td_uni,td_gauss 
   
WEIGHTS
The weights of target distributions. 
=0.25,0.75 
   
...The TD_LINEAR_COMBINATION action with label td_comb

Glossary of keywords and components

Compulsory keywords

DISTRIBUTIONS

The labels of the target distribution actions to be used in the linear combination.

Options

NORMALIZE	( default=off ) Renormalized the target distribution over the intervals on which it is defined to make sure that it is properly normalized to 1. In most cases this should not be needed as the target distributions should be normalized. The code will issue a warning (but still run) if this is needed for some reason.
WEIGHTS	The weights of target distributions. Have to be as many as the number of target distribution labels given in DISTRIBUTIONS. If no weights are given the distributions are weighted equally. The weights are automatically normalized to 1.
WELLTEMPERED_FACTOR	Broaden the target distribution such that it is taken as [p(s)]^(1/ \(\gamma\)) where \(\gamma\) is the well tempered factor given here. If this option is active the distribution will be automatically normalized.