Statistical analysis

Run-time calculations of statistical properties that depend explicitly on time can be performed for individual collective variables. Currently, several types of time correlation functions, running averages and running standard deviations are implemented. For run-time computation of histograms, please see the histogram bias ().

• 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: outputName.$<$ 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: outputName.$<$ name$>$ .runave.traj
  Description: The running average and standard deviation are saved in this file.