This is part of the multicolvar module |
This action can be useed to transform the colvar values calculated by a multicolvar using a histogrambead
In this action each colvar, \(s_i\), calculated by multicolvar is transformed by a histogrambead function that is equal to one if the colvar is within a certain range and which is equal to zero otherwise. In other words, we compute:
\[ f_i = \int_a^b K\left( \frac{s-s_i}{w} \right) \]
where \(a, b\) and \(w\) are parameters.
It is important to understand the distinction between what is done here and what is done by MFILTER_BETWEEN. In MFILTER_BETWEEN a weight, \(w_i\) for the colvar is calculated using the histogrambead. If one calculates the MEAN for MFILTER_BETWEEN one is thus calculating:
\[ \mu = \frac{ \sum_i f_i s_i }{ \sum_i f_i} \]
In this action by contrast the colvar is being transformed by the histogrambead. If one thus calculates a MEAN for thia action one computes:
\[ \mu = \frac{ \sum_{i=1}^N f_i }{ N } \]
In other words, you are calculating the mean for the transformed colvar.
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. |
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 |
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. |
The following input gives an example of how a MTRANSFORM_BETWEEN action can be used to duplicate functionality that is elsehwere in PLUMED.
DISTANCES ... GROUPA=1-10 GROUPB=11-20 LABEL=d1 ... DISTANCES MTRANSFORM_BETWEEN DATA=d1 LOWER=1.0 UPPER=2.0 SMEAR=0.5
In this case you can achieve the same result by using:
DISTANCES ... GROUPA=1-10 GROUPB=11-20 BETWEEN={GAUSSIAN LOWER=1.0 UPPER=2.0} ... DISTANCES
(see DISTANCES)
The advantage of MTRANSFORM_BETWEEN comes, however, if you want to use transformed colvars as input for MULTICOLVARDENS