MTRANSFORM_BETWEEN

This is part of the multicolvar module |

This action can be used 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 this action one computes:

\[ \mu = \frac{ \sum_{i=1}^N f_i }{ N } \]

In other words, you are calculating the mean for the transformed colvar.

- Examples

The following input gives an example of how a MTRANSFORM_BETWEEN action can be used to duplicate functionality that is elsewhere in PLUMED.

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

d1:DISTANCES ...GROUPA=1-10Calculate the distances between all the atoms in GROUPA and all the atoms in GROUPB.GROUPB=11-20 ... MTRANSFORM_BETWEENCalculate the distances between all the atoms in GROUPA and all the atoms in GROUPB.DATA=compulsory keywordThe multicolvar that calculates the set of base quantities that we are interested ind1LOWER=1.0compulsory keywordthe lower boundary for the range of interestUPPER=2.0compulsory keywordthe upper boundary for the range of interestSMEAR=0.5compulsory keyword ( default=0.5 )the amount by which to smear the value for kernel density estimation

In this case you can achieve the same result by using:

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

DISTANCES ...GROUPA=1-10Calculate the distances between all the atoms in GROUPA and all the atoms in GROUPB.GROUPB=11-20Calculate the distances between all the atoms in GROUPA and all the atoms in GROUPB.BETWEEN={GAUSSIAN LOWER=1.0 UPPER=2.0} ...calculate the number of values that are within a certain range.

(see DISTANCES)

The advantage of MTRANSFORM_BETWEEN comes, however, if you want to use transformed colvars as input for MULTICOLVARDENS

- 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. |