Action: TD_LINEAR_COMBINATION

Module	ves
Description	Usage
Target distribution given by linear combination of distributions (static or dynamic).

Details and examples

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_UNIFORMUniform target distribution (static). More details

The TD_UNIFORM action with label td_uni calculates somethingtd_gauss: TD_GAUSSIANTarget distribution given by a sum of Gaussian kernels (static). More details CENTER1The centers of the Gaussian distributions=-2.0 SIGMA1The standard deviations of the Gaussian distributions=0.5

The TD_GAUSSIAN action with label td_gauss calculates somethingtd_comb: TD_LINEAR_COMBINATIONTarget distribution given by linear combination of distributions (static or dynamic). More details DISTRIBUTIONSThe 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 calculates something

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_UNIFORMUniform target distribution (static). More details

The TD_UNIFORM action with label td_uni calculates somethingtd_gauss1: TD_GAUSSIANTarget distribution given by a sum of Gaussian kernels (static). More details CENTER1The centers of the Gaussian distributions=-2.0,-2.0 SIGMA1The standard deviations of the Gaussian distributions=0.5,0.3

The TD_GAUSSIAN action with label td_gauss1 calculates somethingtd_gauss2: TD_GAUSSIANTarget distribution given by a sum of Gaussian kernels (static). More details CENTER1The centers of the Gaussian distributions=+2.0,+2.0 SIGMA1The standard deviations of the Gaussian distributions=0.3,0.5

The TD_GAUSSIAN action with label td_gauss2 calculates somethingTD_LINEAR_COMBINATIONTarget distribution given by linear combination of distributions (static or dynamic). More details ...
 DISTRIBUTIONSThe labels of the target distribution actions to be used in the linear combination=td_uni,td_gauss1,td_gauss2
 WEIGHTSThe weights of target distributions=1.0,1.0,2.0
 LABELa label for the action so that its output can be referenced in the input to other actions=td_comb
... TD_LINEAR_COMBINATION
The TD_LINEAR_COMBINATION action with label td_comb calculates something

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_UNIFORMUniform target distribution (static). More details

The TD_UNIFORM action with label td_uni calculates somethingTD_GAUSSIANTarget distribution given by a sum of Gaussian kernels (static). More details ...
 CENTER1The centers of the Gaussian distributions=-2.0,-2.0  SIGMA1The standard deviations of the Gaussian distributions=0.5,0.3
 CENTER2The centers of the Gaussian distributions=+2.0,+2.0  SIGMA2The standard deviations of the Gaussian distributions=0.3,0.5
 WEIGHTSThe weights of the Gaussian distributions=1.0,2.0
 LABELa label for the action so that its output can be referenced in the input to other actions=td_gauss
... TD_GAUSSIAN

The TD_GAUSSIAN action with label td_gauss calculates somethingTD_LINEAR_COMBINATIONTarget distribution given by linear combination of distributions (static or dynamic). More details ...
 DISTRIBUTIONSThe labels of the target distribution actions to be used in the linear combination=td_uni,td_gauss
 WEIGHTSThe weights of target distributions=0.25,0.75
 LABELa label for the action so that its output can be referenced in the input to other actions=td_comb
... TD_LINEAR_COMBINATION
The TD_LINEAR_COMBINATION action with label td_comb 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
DISTRIBUTIONS	compulsory	none	The labels of the target distribution actions to be used in the linear combination
WEIGHTS	optional	not used	The weights of target distributions
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
NORMALIZEThis keyword do not have examples	optional	false	Renormalized the target distribution over the intervals on which it is defined to make sure that it is properly normalized to 1