COLUMNSUMS

This is part of the adjmat module | |

It is only available if you configure PLUMED with ./configure –enable-modules=adjmat . Furthermore, this feature is still being developed so take care when using it and report any problems on the mailing list. |

Sum the columns of a contact matrix

As discussed in the section of the manual on Exploiting contact matrices a useful tool for developing complex collective variables is the notion of the so called adjacency matrix. An adjacency matrix is an \(N \times N\) matrix in which the \(i\)th, \(j\)th element tells you whether or not the \(i\)th and \(j\)th atoms/molecules from a set of \(N\) atoms/molecules are adjacent or not. This action allows you to calculate the sum of the columns in this adjacency matrix and to then calculate further functions of these quantities.

- Examples

The first instruction in the following input file tells PLUMED to compute a \(10 \times 10\) matrix in which the \(ij\)-element tells you whether atoms \(i\) and \(j\) are within 1.0 nm of each other. The numbers in each of this rows are then added together and the average value is computed. As such the following input provides an alternative method for calculating the coordination numbers of atoms 1 to 10.

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

mat:CONTACT_MATRIXATOMS=1-10The list of atoms for which you would like to calculate the contact matrix.SWITCH={RATIONAL R_0=1.0}This keyword is used if you want to employ an alternative to the continuous switching function defined above.rsums:COLUMNSUMSMATRIX=compulsory keywordthe action that calculates the adjacency matrix vessel we would like to analyzematMEANPRINTtake the mean of these variables.ARG=the input for this action is the scalar output from one or more other actions.rsums.*FILE=colvarthe name of the file on which to output these quantities

The following input demonstrates another way that an average coordination number can be computed. This input calculates the number of atoms with indices between 1 and 5 that are within the first coordination spheres of each of the atoms within indices between 6 and 15. The average coordination number is then calculated from these fifteen coordination numbers and this quantity is output to a file.

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

mat2:CONTACT_MATRIXATOMSA=1-5ATOMSB=6-15SWITCH={RATIONAL R_0=1.0}This keyword is used if you want to employ an alternative to the continuous switching function defined above.rsums:COLUMNSUMSMATRIX=compulsory keywordthe action that calculates the adjacency matrix vessel we would like to analyzemat2MEANPRINTtake the mean of these variables.ARG=the input for this action is the scalar output from one or more other actions.rsums.*FILE=colvarthe name of the file on which to output these quantities

- 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 |

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. |

between | BETWEEN | the number/fraction of values within a certain range. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters. |

highest | HIGHEST | the highest of the quantities calculated by this action |

lessthan | LESS_THAN | the number of values less than a target value. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters. |

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. |

morethan | MORE_THAN | the number of values more than a target value. This is calculated using one of the formula described in the description of the keyword so as to make it continuous. You can calculate this quantity multiple times using different parameters. |

- Compulsory keywords

MATRIX | the action that calculates the adjacency matrix vessel we would like to analyze |

- 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 |

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 |

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... |

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... |

LESS_THAN | calculate the number of variables less than a certain target value. This quantity is calculated using \(\sum_i \sigma(s_i)\), where \(\sigma(s)\) is a switchingfunction. The final value can be referenced using label.lessthan. You can use multiple instances of this keyword i.e. LESS_THAN1, LESS_THAN2, LESS_THAN3... The corresponding values are then referenced using label.lessthan-1, label.lessthan-2, label.lessthan-3... |

MORE_THAN | calculate the number of variables more than a certain target value. This quantity is calculated using \(\sum_i 1.0 - \sigma(s_i)\), where \(\sigma(s)\) is a switchingfunction. The final value can be referenced using label.morethan. You can use multiple instances of this keyword i.e. MORE_THAN1, MORE_THAN2, MORE_THAN3... The corresponding values are then referenced using label.morethan-1, label.morethan-2, label.morethan-3... |

BETWEEN | calculate the number of values that are within a certain range. These quantities are calculated using kernel density estimation as described on histogrambead. The final value can be referenced using label.between. You can use multiple instances of this keyword i.e. BETWEEN1, BETWEEN2, BETWEEN3... The corresponding values are then referenced using label.between-1, label.between-2, label.between-3... |

HISTOGRAM | calculate how many of the values fall in each of the bins of a histogram. This shortcut allows you to calculates NBIN quantities like BETWEEN. The final value can be referenced using label.histogram. You can use multiple instances of this keyword i.e. HISTOGRAM1, HISTOGRAM2, HISTOGRAM3... The corresponding values are then referenced using label.histogram-1, label.histogram-2, label.histogram-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... |