getMeanTransitTime_method__ConstLinDecompOp: compute the mean transit time
Description
This method computes the mean transit time for the linear time invariant system
that can be constructed from the given operator and input distribution.
It relies on the mehtod getTransitTimeDistributionDensity using the same arguments.Details
To compute the mean transit time for the distribution we have to compute the integral
$$\bar{T} = \int_0^\infty T \cdot S_r\left( \frac{\vec{I}}{I},0,T\right)\; dT$$
for the numerically computed density.
To avoid issues with numerical integration we dont use $\infty$ as upper limit but cut off the integragion interval prematurely.
For this purpose we calculate a maximum response time of the system as Lasaga
$$\tau_{cycle} = \frac{1}{|\min(\lambda_i)|}$$
where $\lambda_i$ are non-zero eigenvalues of the matrix
${\bf A}$.References
Lasaga, A.: The kinetic treatment of geochemical cycles, Geochimica et
Cosmochimica Acta, 44, 815 -- 828, doi{10.1016/0016-7037(80)90263-X}, 1980.