Linear Autonomous Pool Models (LAPM)¶
LAPM is a simple Python package to deal with linear autonomous pool models of the form
\[\frac{d}{dt}\,x(t) = B\,x(t) + u.\]
It provides symbolic and numerical computation of
steady state content
steady state release
transit time, system age, pool age
- density
- (cumulative distribution function)
- mean
- standard deviation
- variance
- higher order moments
- (Laplace transforms)
Table of Contents¶
phase_type |
Module for phase-type distribution. |
linear_autonomous_pool_model |
Module for linear autonomous pool models. |
dtmc |
Module for discrete-time Markov chains (DTMCs). |
example_models |
Example linear autonomous pool models. |
emanuel |
Example: Emanuel’s model |
Important Note¶
\(\bf{B}=(b_{ij})\) has always to be an invertible compartmental matrix:
- \(b_{ii}<0\) for all \(i\)
- \(b_{ij}\geq 0\) for \(i\neq j\)
- \(\sum\limits_{i=1}^d b_{ij}\leq 0\) for all \(j\)