Statistical analysis of collective variables

When the global keyword analysis is defined in the configuration file, run-time calculations of statistical properties for individual colvars can be performed. At the moment, several types of time correlation functions, running averages and running standard deviations are available.

• corrFunc $\langle\,$ Calculate a time correlation function?$\,\rangle$
  Context: colvar
  Acceptable values: boolean
  Default value: off
  Description: Whether or not a time correlaction function should be calculated for this colvar.

• corrFuncWithColvar $\langle\,$ Colvar name for the correlation function$\,\rangle$
  Context: colvar
  Acceptable values: string
  Description: By default, the auto-correlation function (ACF) of this colvar, $\xi_{i}$ , is calculated. When this option is specified, the correlation function is calculated instead with another colvar, $\xi_{j}$ , which must be of the same type (scalar, vector, or quaternion) as $\xi_{i}$ .

• corrFuncType $\langle\,$ Type of the correlation function$\,\rangle$
  Context: colvar
  Acceptable values: velocity, coordinate or coordinate_p2
  Default value: velocity
  Description: With coordinate or velocity, the correlation function $C_{i,j}(t)$  = $\left\langle \Pi\left(\xi_{i}(t_{0}), \xi_{j}(t_{0}+t)\right) \right\rangle$ is calculated between the variables $\xi_{i}$ and $\xi_{j}$ , or their velocities. $\Pi(\xi_{i}, \xi_{j})$ is the scalar product when calculated between scalar or vector values, whereas for quaternions it is the cosine between the two corresponding rotation axes. With coordinate_p2, the second order Legendre polynomial, $(3\cos(\theta)^{2}-1)/2$ , is used instead of the cosine.

• corrFuncNormalize $\langle\,$ Normalize the time correlation function?$\,\rangle$
  Context: colvar
  Acceptable values: boolean
  Default value: on
  Description: If enabled, the value of the correlation function at $t$  = 0 is normalized to 1; otherwise, it equals to $\left\langle O\left(\xi_{i}, \xi_{j}\right) \right\rangle$ .

• corrFuncLength $\langle\,$ Length of the time correlation function$\,\rangle$
  Context: colvar
  Acceptable values: positive integer
  Default value: 1000
  Description: Length (in number of points) of the time correlation function.

• corrFuncStride $\langle\,$ Stride of the time correlation function$\,\rangle$
  Context: colvar
  Acceptable values: positive integer
  Default value: 1
  Description: Number of steps between two values of the time correlation function.

• corrFuncOffset $\langle\,$ Offset of the time correlation function$\,\rangle$
  Context: colvar
  Acceptable values: positive integer
  Default value: 0
  Description: The starting time (in number of steps) of the time correlation function (default: $t$  = 0). Note: the value at $t$  = 0 is always used for the normalization.

• corrFuncOutputFile $\langle\,$ Output file for the time correlation function$\,\rangle$
  Context: colvar
  Acceptable values: UNIX filename
  Default value: $<$ name$>$ .corrfunc.dat
  Description: The time correlation function is saved in this file.

• runAve $\langle\,$ Calculate the running average and standard deviation$\,\rangle$
  Context: colvar
  Acceptable values: boolean
  Default value: off
  Description: Whether or not the running average and standard deviation should be calculated for this colvar.

• runAveLength $\langle\,$ Length of the running average window$\,\rangle$
  Context: colvar
  Acceptable values: positive integer
  Default value: 1000
  Description: Length (in number of points) of the running average window.

• runAveStride $\langle\,$ Stride of the running average window values$\,\rangle$
  Context: colvar
  Acceptable values: positive integer
  Default value: 1
  Description: Number of steps between two values within the running average window.

• runAveOutputFile $\langle\,$ Output file for the running average and standard deviation$\,\rangle$
  Context: colvar
  Acceptable values: UNIX filename
  Default value: $<$ name$>$ .runave.dat
  Description: The running average and standard deviation are saved in this file.