MFILTER_BETWEEN
This is part of the multicolvar module

This action can be used to filter the colvar values calculated by a MultiColvar so that one can compute the mean and so on for only those multicolvars within a certain range.

This action can be used to create a dynamic group of atom based on the value of a multicolvar. In this action a multicolvar is within the dynamic group if its value lies in a particular range. In actuality a weight, \(w_i\) is ascribed to each colvar, \(s_i\) calculated by a multicolvar and this weight measures the degree to which a colvar is a member of the group. This weight is calculated using a histogrambead so it is given by:

\[ w_i = \int_a^b K\left( \frac{s - s_i}{w} \right) \]

where \(a, b\) and \(w\) are parameters. If one calculates a function of the set of multicolvars these weights are included in the calculation. As such if one calculates the MEAN, \(\mu\) of a filtered multicolvar what is computed is the following:

\[ \mu = \frac{ \sum_i w_i s_i }{ \sum_i w_i} \]

One is thus calculating the mean for those colvars that are within the range of interest.

Examples

The example shown below calculates the mean for those distances that are between 0 and 3 nm in length

Click on the labels of the actions for more information on what each action computes
tested on master
d1: DISTANCES 
GROUPA
Calculate the distances between all the atoms in GROUPA and all the atoms in GROUPB.
=1
GROUPB
Calculate the distances between all the atoms in GROUPA and all the atoms in GROUPB.
=2-50
MEAN
take the mean of these variables.
d4: MFILTER_BETWEEN
DATA
compulsory keyword The multicolvar that calculates the set of base quantities that we are interested in
=d1
LOWER
compulsory keyword the lower boundary for the range of interest
=0
UPPER
compulsory keyword the upper boundary for the range of interest
=3.0
SMEAR
compulsory keyword ( default=0.5 ) the amount by which to smear the value for kernel density estimation
=0.0001
MEAN
take the mean of these variables.

More complicated things can be done by using the label of a filter as input to a new multicolvar as shown in the example below. Here the coordination numbers of all atoms are computed. The atoms with a coordination number between 4 and 6 are then identified using the filter. This reduced list of atoms is then used as input to a second coordination number calculation. This second coordination number thus measures the number of atoms 4-6 coordinated atoms each of the 4-6 coordination atoms is bound to.

Click on the labels of the actions for more information on what each action computes
tested on master
c1: COORDINATIONNUMBER 
SPECIES
this keyword is used for colvars such as coordination number.
=1-150
SWITCH
This keyword is used if you want to employ an alternative to the continuous switching function defined above.
={EXP D_0=4.0 R_0=0.5 D_MAX=6.0} cf: MFILTER_BETWEEN
DATA
compulsory keyword The multicolvar that calculates the set of base quantities that we are interested in
=c1
LOWER
compulsory keyword the lower boundary for the range of interest
=4
UPPER
compulsory keyword the upper boundary for the range of interest
=6
SMEAR
compulsory keyword ( default=0.5 ) the amount by which to smear the value for kernel density estimation
=0.5
LOWMEM
( default=off ) lower the memory requirements
c2: COORDINATIONNUMBER
SPECIES
this keyword is used for colvars such as coordination number.
=cf
SWITCH
This keyword is used if you want to employ an alternative to the continuous switching function defined above.
={EXP D_0=4.0 R_0=0.5 D_MAX=6.0}
MORE_THAN
calculate the number of variables more than a certain target value.
={RATIONAL D_0=2.0 R_0=0.1}
Glossary of keywords and components
Description of components

When the label of this action is used as the input for a second you are not referring to a scalar quantity as you are in regular collective variables. The label is used to reference the full set of quantities calculated by the action. This is usual when using MultiColvar functions. Generally when doing this the previously calculated multicolvar will be referenced using the DATA keyword rather than ARG.

This Action can be used to calculate the following scalar quantities directly. These quantities are calculated by employing the keywords listed below. These quantities can then be referenced elsewhere in the input file by using this Action's label followed by a dot and the name of the quantity. Some of them can be calculated multiple times with different parameters. In this case the quantities calculated can be referenced elsewhere in the input by using the name of the quantity followed by a numerical identifier e.g. label.lessthan-1, label.lessthan-2 etc. When doing this and, for clarity we have made it so that the user can set a particular label for each of the components. As such by using the LABEL keyword in the description of the keyword input you can customize the component name

Quantity Keyword Description
vmean VMEAN the norm of the mean vector. The output component can be referred to elsewhere in the input file by using the label.vmean
altmin ALT_MIN the minimum value. This is calculated using the formula described in the description of the keyword so as to make it continuous.
highest HIGHEST the highest of the quantities calculated by this action
lowest LOWEST the lowest of the quantities calculated by this action
max MAX the maximum value. This is calculated using the formula described in the description of the keyword so as to make it continuous.
mean MEAN the mean value. The output component can be referred to elsewhere in the input file by using the label.mean
min MIN the minimum value. This is calculated using the formula described in the description of the keyword so as to make it continuous.
moment MOMENTS the central moments of the distribution of values. The second moment would be referenced elsewhere in the input file using label.moment-2, the third as label.moment-3, etc.
Compulsory keywords
DATA The multicolvar that calculates the set of base quantities that we are interested in
LOWER the lower boundary for the range of interest
UPPER the upper boundary for the range of interest
SMEAR ( default=0.5 ) the amount by which to smear the value for kernel density estimation
Options
NUMERICAL_DERIVATIVES ( default=off ) calculate the derivatives for these quantities numerically
NOPBC ( default=off ) ignore the periodic boundary conditions when calculating distances
SERIAL ( default=off ) do the calculation in serial. Do not use MPI
LOWMEM ( default=off ) lower the memory requirements
TIMINGS

( default=off ) output information on the timings of the various parts of the calculation

VMEAN calculate the norm of the mean vector. The final value can be referenced using label.vmean. You can use multiple instances of this keyword i.e. VMEAN1, VMEAN2, VMEAN3... The corresponding values are then referenced using label.vmean-1, label.vmean-2, label.vmean-3...
MEAN take the mean of these variables. The final value can be referenced using label.mean. You can use multiple instances of this keyword i.e. MEAN1, MEAN2, MEAN3... The corresponding values are then referenced using label.mean-1, label.mean-2, label.mean-3...
MOMENTS calculate the moments of the distribution of collective variables. The mth moment of a distribution is calculated using \(\frac{1}{N} \sum_{i=1}^N ( s_i - \overline{s} )^m \), where \(\overline{s}\) is the average for the distribution. The moments keyword takes a lists of integers as input or a range. Each integer is a value of \(m\). The final calculated values can be referenced using moment- \(m\). You can use the COMPONENT keyword in this action but the syntax is slightly different. If you would like the second and third moments of the third component you would use MOMENTS={COMPONENT=3 MOMENTS=2-3}. The moments would then be referred to using the labels moment-3-2 and moment-3-3. This syntax is also required if you are using numbered MOMENT keywords i.e. MOMENTS1, MOMENTS2...
MIN calculate the minimum value. To make this quantity continuous the minimum is calculated using \( \textrm{min} = \frac{\beta}{ \log \sum_i \exp\left( \frac{\beta}{s_i} \right) } \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\)) The final value can be referenced using label.min. You can use multiple instances of this keyword i.e. MIN1, MIN2, MIN3... The corresponding values are then referenced using label.min-1, label.min-2, label.min-3...
MAX calculate the maximum value. To make this quantity continuous the maximum is calculated using \( \textrm{max} = \beta \log \sum_i \exp\left( \frac{s_i}{\beta}\right) \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\)) The final value can be referenced using label.max. You can use multiple instances of this keyword i.e. MAX1, MAX2, MAX3... The corresponding values are then referenced using label.max-1, label.max-2, label.max-3...
ALT_MIN calculate the minimum value. To make this quantity continuous the minimum is calculated using \( \textrm{min} = -\frac{1}{\beta} \log \sum_i \exp\left( -\beta s_i \right) \) The value of \(\beta\) in this function is specified using (BETA= \(\beta\)). The final value can be referenced using label.altmin. You can use multiple instances of this keyword i.e. ALT_MIN1, ALT_MIN2, ALT_MIN3... The corresponding values are then referenced using label.altmin-1, label.altmin-2, label.altmin-3...
LOWEST this flag allows you to recover the lowest of these variables. The final value can be referenced using label.lowest
HIGHEST this flag allows you to recover the highest of these variables. The final value can be referenced using label.highest
BEAD This keywords is used if you want to employ an alternative to the function defined above. The following provides information on the histogrambead that are available. When this keyword is present you no longer need the LOWER, UPPER and SMEAR keywords.