Compute volume contraction of the Jacobian matrics

We define the volume contraction as the rate at which an infinitesimal volume scales through the Jacobian. This can be calculated as the determinant of the Jacobian (i.e. the product of the eigenvalues or singular values, which represent the scaling along various directions in the state space).

compute_volume_contraction(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 volume contraction 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 |det(J_s