   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 practise 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.

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 amongst 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 the label of the components customizable. 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 refererred 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 lowest of the quantitities calculated by this action lowest LOWEST the lowest of the quantitities 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 refererred 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 ammount 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 parallelize 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 $$m$$th 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- $$m$$. 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 defeind 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.
Examples

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

DISTANCES GROUPA=1 GROUPB=2-50 MEAN LABEL=d1
MFILTER_BETWEEN DATA=d1 LOWER=0 UPPER=3.0 SMEAR=0.0001 MEAN LABEL=d4


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.

c1: COORDINATIONNUMBER SPECIES=1-150 SWITCH={EXP D_0=4.0 R_0=0.5 D_MAX=6.0}
cf: MFILTER_BETWEEN DATA=c1 LOWER=4 UPPER=6 SMEAR=0.5 LOWMEM
c2: COORDINATIONNUMBER SPECIES=cf SWITCH={EXP D_0=4.0 R_0=0.5 D_MAX=6.0} MORE_THAN={RATIONAL D_0=2.0 R_0=0.1}