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}.
eD2
a tensor with all estimated errors of the driffusion
coefficient. Dimension is bins x bins x 3. Same expression as
above.
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).