Action: REWEIGHT_BIAS

Module	bias
Description	Usage
Calculate weights for ensemble averages that negate the effect the bias has on the region of phase space explored
output value	type
the weight to use for this frame to negate the effect the bias	scalar

Details and examples

Calculate weights for ensemble averages that negate the effect the bias has on the region of phase space explored

If a static or pseudo-static bias $V(x,t')$ is acting on the system we can remove the bias and get the unbiased probability distribution using:

$$\langle P(s',t) \rangle = \frac{ \sum_{t'}^t \delta( s(x) - s' ) \exp\left( +\frac{V(x,t')}{k_B T} \right) }{ \sum_t'^t \exp\left( +\frac{V(x,t')}{k_B T} \right) }$$

The weights calculated by this action are equal to $\exp\left( +\frac{V(x,t')}{k_B T} \right)$ these weights can then be used in any action that computes ensemble averages. For example this action can be used in tandem with HISTOGRAM or AVERAGE.

Examples

In the following example there is a fixed restraint on the distance between atoms 1 and 2. Clearly, this restraint will have an effect on the region of phase space that will be sampled when an MD simulation is run using this variable. Consequently, when the histogram as a function of the distance, $x$, is accumulated, we use reweighting into order to discount the effect of the bias from our final histogram.

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

xThe DISTANCE action with label x calculates the following quantities:
 Quantity   
 Type   
 Description  
x
scalar
the DISTANCE between this pair of atoms: DISTANCECalculate the distance/s between pairs of atoms. More details ATOMSthe pair of atom that we are calculating the distance between=1,2
RESTRAINTAdds harmonic and/or linear restraints on one or more variables. More details ARGthe values the harmonic restraint acts upon=x SLOPE specifies that the restraint is linear and what the values of the force constants on each of the variables are=1.0 ATthe position of the restraint=0.0
The RESTRAINT action with label  calculates the following quantities:
 Quantity   
 Description  
.bias
the instantaneous value of the bias potential
.force2
the instantaneous value of the squared force due to this bias potentialbiasThe REWEIGHT_BIAS action with label bias calculates the following quantities:
 Quantity   
 Type   
 Description  
bias
scalar
the weight to use for this frame to negate the effect the bias: REWEIGHT_BIASCalculate weights for ensemble averages that negate the effect the bias has on the region of phase space explored This action has hidden defaults. More details TEMPthe system temperature=300
bias: REWEIGHT_BIASCalculate weights for ensemble averages that negate the effect the bias has on the region of phase space explored This action uses the defaults shown here. More details TEMPthe system temperature=300  ARG the biases that must be taken into account when reweighting=*.bias

hBThe HISTOGRAM action with label hB calculates the following quantities:
 Quantity   
 Type   
 Description  
hB
grid
the estimate of the histogram as a function of the argument that was obtained: HISTOGRAMAccumulate the average probability density along a few CVs from a trajectory. This action is a shortcut and it has hidden defaults. More details ...
  ARGthe quantities that are being used to construct the histogram=x
  GRID_MIN the lower bounds for the grid=0.0
  GRID_MAX the upper bounds for the grid=3.0
  GRID_BINthe number of bins for the grid=100
  BANDWIDTHthe bandwidths for kernel density esimtation=0.1
  LOGWEIGHTSthe logarithm of the quantity to use as the weights when calculating averages=bias
...
hB: HISTOGRAMAccumulate the average probability density along a few CVs from a trajectory. This action is a shortcut and uses the defaults shown here. More details ...
  ARGthe quantities that are being used to construct the histogram=x
  GRID_MIN the lower bounds for the grid=0.0
  GRID_MAX the upper bounds for the grid=3.0
  GRID_BINthe number of bins for the grid=100
  BANDWIDTHthe bandwidths for kernel density esimtation=0.1
  LOGWEIGHTSthe logarithm of the quantity to use as the weights when calculating averages=bias
 NORMALIZATION This controls how the data is normalized it can be set equal to true, false or ndata=ndata STRIDE the frequency with which to store data for averaging=1 CLEAR the frequency with whihc to clear the data that is being averaged=0
...
# PLUMED interprets the command:
# hB: HISTOGRAM ...
#   ARG=x
#   GRID_MIN=0.0
#   GRID_MAX=3.0
#   GRID_BIN=100
#   BANDWIDTH=0.1
#   LOGWEIGHTS=bias
# ...
# as follows (Click the red comment above to revert to the short version of the input):
hB_weightThe CONSTANT action with label hB_weight calculates the following quantities:
 Quantity   
 Type   
 Description  
hB_weight
scalar
the constant value that was read from the plumed input: ONESCreate a constant vector with all elements equal to one More details SIZEthe number of ones that you would like to create=1
hB_kdeThe KDE action with label hB_kde calculates the following quantities:
 Quantity   
 Type   
 Description  
hB_kde
grid
a function on a grid that was obtained by doing a Kernel Density Estimation using the input arguments: KDECreate a histogram from the input scalar/vector/matrix using KDE More details ARGthe label for the value that should be used to construct the histogram=x  BANDWIDTHthe bandwidths for kernel density esimtation=0.1 GRID_BINthe number of bins for the grid=100 GRID_MAX the upper bounds for the grid=3.0 GRID_MIN the lower bounds for the grid=0.0
hB_kdepThe CUSTOM action with label hB_kdep calculates the following quantities:
 Quantity   
 Type   
 Description  
hB_kdep
grid
the grid obtained by doing an element-wise application of an arbitrary function to the input grid: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=hB_kde,hB_weight FUNCthe function you wish to evaluate=x*y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
hB_uThe ACCUMULATE action with label hB_u calculates the following quantities:
 Quantity   
 Type   
 Description  
hB_u
grid
a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory More details ARGthe label of the argument that is being added to on each timestep=hB_kdep STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0 
hB_nsumThe ACCUMULATE action with label hB_nsum calculates the following quantities:
 Quantity   
 Type   
 Description  
hB_nsum
scalar
a sum calculated from the time series of the input quantity: ACCUMULATESum the elements of this value over the course of the trajectory More details ARGthe label of the argument that is being added to on each timestep=hB_weight STRIDE the frequency with which the data should be collected and added to the quantity being averaged=1 CLEAR the frequency with which to clear all the accumulated data=0 
hBThe CUSTOM action with label hB calculates the following quantities:
 Quantity   
 Type   
 Description  
hB
grid
the grid obtained by doing an element-wise application of an arbitrary function to the input grid: CUSTOMCalculate a combination of variables using a custom expression. More details ARGthe values input to this function=hB_u,hB_nsum FUNCthe function you wish to evaluate=x/y PERIODICif the output of your function is periodic then you should specify the periodicity of the function=NO
# --- End of included input --- 
DUMPGRIDOutput the function on the grid to a file with the PLUMED grid format. More details ARGthe label for the grid that you would like to output=hB FILE the file on which to write the grid=histoB STRIDE the frequency with which the grid should be output to the file=1

Input

The arguments that serve as the input for this action are specified using one or more of the keywords in the following table.

Keyword	Type	Description
ARG	scalar	the biases that must be taken into account when reweighting

Full list of keywords

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

Keyword	Type	Default	Description
ARG	input	none	the biases that must be taken into account when reweighting
TEMP	optional	not used	the system temperature