Langevin2D: Calculate the Drift and Diffusion of two-dimensional...

In Langevin: Langevin Analysis in One and Two Dimensions

Description

Langevin2D calculates the Drift (with error) and Diffusion matrices for given time series.

Usage

Langevin2D(
  data,
  bins,
  steps,
  sf = ifelse(is.mts(data), frequency(data), 1),
  bin_min = 100,
  reqThreads = -1
)

Arguments

data	a matrix containing the time series as columns or a time-series object.
bins	a scalar denoting the number of bins to calculate Drift and Diffusion on.
steps	a vector giving the τ steps to calculate the moments (in samples).
sf	a scalar denoting the sampling frequency (optional if data is a time-series object).
bin_min	a scalar denoting the minimal number of events per bin. Defaults to 100.
reqThreads	a scalar denoting how many threads to use. Defaults to -1 which means all available cores.

Value

Langevin2D returns a list with nine components:

D1	a tensor with all values of the drift coefficient. Dimension is bins x bins x 2. The first bins x bins elements define the drift D^{(1)}_{1} for the first variable and the rest define the drift D^{(1)}_{2} for the second variable.
eD1	a tensor with all estimated errors of the drift coefficient. Dimension is bins x bins x 2. Same expression as above.
D2	a tensor with all values of the diffusion coefficient. Dimension is bins x bins x 3. The first bins x bins elements define the diffusion D^{(2)}_{11}, the second bins x bins elements define the diffusion D^{(2)}_{22} and the rest define the diffusion D^{(2)}_{12} = D^{(2)}_{21}.
mean_bin	a matrix of the mean value per bin. Dimension is bins x bins x 2. The first bins x bins elements define the mean for the first variable and the rest for the second variable.
density	a matrix of the number of events per bin. Rows label the bin of the first variable and columns the second variable.
M1	a tensor of the first moment for each bin (line label) and each τ step (column label). Dimension is bins x bins x 2length(steps).
eM1	a tensor of the standard deviation of the first moment for each bin (line label) and each τ step (column label). Dimension is bins x bins x 2length(steps).
M2	a tensor of the second moment for each bin (line label) and each τ step (column label). Dimension is bins x bins x 3length(steps).
U	a matrix of the bin borders

Author(s)

Philip Rinn

See Also

Langevin1D

Langevin documentation built on Oct. 19, 2021, 5:06 p.m.