Compute total variance of the Jacobian matrics

We define the total variance as the variance that results when applying the Jacobian to a point with zero mean and unit variance. This can be calculated as the trace of the Jacobian multiplied by its transpose. The diagonal elements then represent the variance of each dimension, with off- diagonal elements being the covariance.

compute_total_variance(smap_matrices, s = NULL)

Arguments

smap_matrices	A list with the Jacobian matrix (of smap-coefficients) at each time point, resulting from compute_smap_matrices()
s	the number of species in the system (optional parameter to restrict the analysis just to the portions of the Jacobian that are relevant for the forecasts)

Value

a numeric vector of the total variance values

Details

See compute_svd_decomp() for details on extracting the portion of the Jacobian used for calculating the determinant.

We do this in order to account for the low-rank of the full Jacobian, which otherwise results in a determinant of 0.

We then compute the pseudo-determinant as Tr(J_s