TD_PRODUCT_DISTRIBUTION
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 a separable product of one-dimensional distributions (static or dynamic).

Employ a target distribution that is a separable product of one-dimensional distributions, defined as

\[ p(\mathbf{s}) = \prod_{k}^{d} p_{k}(s_{k}) \]

where \(d\) is the number of arguments used and \(p_{k}(s_{k})\) is the one-dimensional distribution corresponding to the \(k\)-th argument.

Note the difference between this target distribution and the one defined in TD_PRODUCT_COMBINATION. Here we have a separable distribution given as a product of one-dimensional distribution \(p_{k}(s_{k})\).

The labels of the one-dimensional distributions \(p_{k}(s_{k})\) to be used in the product distribution are given in the DISTRIBUTIONS keyword. Note that the order of the labels is very important.

It is assumed that all the distributions to be used in the product distribution are normalized. If that is not the case you need to normalize the distributions by using the NORMALIZE keyword. Here it does not matter if you normalize each distribution separately or the overall product, it will give the same results.

The product distribution 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.

Compulsory keywords
DISTRIBUTIONS Labels of the one-dimensional target distribution actions for each argument to be used in the product distribution. Note that order of the labels is important.
Options
SHIFT_TO_ZERO ( default=off ) Shift the minimum value of the target distribution to zero. This can for example be used to avoid negative values in the target distribution. If this option is active the distribution will be automatically normalized.
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.

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.
Examples

In the following example we employ a uniform distribution for argument 1 and a Gaussian distribution for argument 2.

target_uniform: TD_UNIFORM

target_Gaussian: TD_GAUSSIAN CENTER1=-2.0 SIGMA1=0.5

td_pd: TD_PRODUCT_DISTRIBUTION DISTRIBUTIONS=target_uniform,target_Gaussian

Note that order of the labels is important, using DISTRIBUTIONS=target_Gaussian,target_uniform would mean that we would employ a Gaussian distribution for argument 1 and a uniform distribution for argument 2, which would lead to completely different results.