Performs the S-map on a univariate time series to infer the Jacobian matrix at different points in time across thetas.

## Source

Grziwotz, F., Chang, C.-W., Dakos, V., van Nes, E.H., Schwarzländer, M., Kamps, O., et al. (2023). Anticipating the occurrence and type of critical transitions. Science Advances, 9.

## Arguments

- data
Numeric matrix with time in first column and species abundance in the second

- theta_seq
Numeric vector of thetas (nonlinear tuning parameters) to estimate the Jacobian over. If `NULL`, a default sequence is provided.

- E
Numeric. The embedding dimension. Is suggested to be positive.

- tau
Numeric. The time-delay offset to use for time delay embedding. Suggested to be positive here, but if not provided, is set to 10% the length of the time series.

- scale
Boolean. Should data be scaled prior to estimating the Jacobian.

## Value

A list containing three objects:

- smap_J
Jacobian matrices across taus. It is recommended to average across these matrices.

- eigenJ
Absolute maximum eigenvalue.

- reJ
Real component of dominant eigenvalue

- imJ
Imaginary component of dominant eigenvalue.

## Examples

```
#Load the multivariate simulated
#dataset `simTransComms`
data("simTransComms")
#Subset the second community prior to the transition
pre_simTransComms <- subset(simTransComms$community2,time < inflection_pt)
winsize <- round(dim(pre_simTransComms)[1] * 50/100)
#Estimate the Jacobian for the first 50 timepoints of the
#second species using s-map
est_jac <- uni_smap_jacobian(pre_simTransComms[1:50,2:3])
```