This python package is intended to be used for the computation of the analytic center of a strictly passive and stable discrete-time or continuous-time linear time-invariant system. One can choose between several solvers (Newton, steepest ascent). Note that this package is research code and a proof-of-concept implementation. There is no guaranty for robustness or optimality of the code. Please cite this code, when using for your publication results.
The package can be installed by running
python setup.py install
after fulfilling the requirements listed in setup.py.
Note that you need at least python version 3.5 to use this software.
Alternatively, you can install the conda package by invoking
conda install -c conda-forge -c dbankmann analyticcenter
The following simple example can be found in examples/example3.py.
Run the example with python3 -O examples/example3.py or with python3 -O -m analyticcenter.examples.example3. Ommiting the -O switch will turn on some debugging information.
- First one has to create a system object
sys:
import numpy as np
from analyticcenter import WeightedSystem
A = np.matrix([[1, -1], [1, 1]])
B = np.matrix([[1], [1]])
C = B.T
D = C @ B
Q = np.zeros((2,2))
sys = WeightedSystem(A, B, C, D, Q, B, D + D.T)- Then one has to create an algorithm object, where you have to define the type of the system (discrete, continuous) and you can optionally provide some tolerances.
from analyticcenter import get_algorithm_object
from analyticcenter.examples.example2 import sys
if __name__ == "__main__":
alg = get_algorithm_object(sys, 'newton', discrete_time=False, save_intermediate=True)
alg()- The resulting analytic center object
accontains data and methods for analyzing the system at the analytic center.
There are a few jupyter notebooks in the examples folder showing all the results (and more) that are used in the references below.
Some tests for the basic functionality have been written. You can run those with
python setup.py test
Uses pythons logging module. Configuration can be found in config/config.yaml. If the package should be used as a library, the automatic configuration should be disabled by uncommenting the appropriate line in __init__.py.
See the provided license file.
Daniel Bankmann
Technische Universität Berlin
bankmann@math.tu-berlin.de
Bankmann, D.; Mehrmann, V.; Nesterov, Y.; van Dooren, P., "Computation of the analytic center of the solution set of the linear matrix inequality arising in continuous- and discrete-time passivity analysis, 2019"
C. A. Beattie, V. Mehrmann, and P. Van Dooren, “Robust port-Hamiltonian representations of passive systems,” Automatica, vol. 100, pp. 182–186, Feb. 2019.