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| 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.
| DISTRIBUTIONS | The labels of the target distribution actions to be used in the linear combination. |
| 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. |
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.
td_uni: TD_UNIFORM td_gauss: TD_GAUSSIAN CENTER1=-2.0 SIGMA1=0.5 td_comb: TD_LINEAR_COMBINATION DISTRIBUTIONS=td_uni,td_gauss
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.
td_uni: TD_UNIFORM td_gauss1: TD_GAUSSIAN CENTER1=-2.0,-2.0 SIGMA1=0.5,0.3 td_gauss2: TD_GAUSSIAN CENTER1=+2.0,+2.0 SIGMA1=0.3,0.5 TD_LINEAR_COMBINATION ... DISTRIBUTIONS=td_uni,td_gauss1,td_gauss2 WEIGHTS=1.0,1.0,2.0 LABEL=td_comb ... TD_LINEAR_COMBINATION
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
td_uni: TD_UNIFORM TD_GAUSSIAN ... CENTER1=-2.0,-2.0 SIGMA1=0.5,0.3 CENTER2=+2.0,+2.0 SIGMA2=0.3,0.5 WEIGHTS=1.0,2.0 LABEL=td_gauss ... TD_GAUSSIAN TD_LINEAR_COMBINATION ... DISTRIBUTIONS=td_uni,td_gauss WEIGHTS=0.25,0.75 LABEL=td_comb ... TD_LINEAR_COMBINATION
1.8.14