Spring packets example

We take an example of a fault tolerant system, where a few masses are coupled via packets of springs. Each spring has the same failure probability independent of its age. This leads to a Markov chain. Its transition matrix can be computed with the module Spring packets:

>>> import spring_packets
>>> from mcst import scenario_tree_from_markov_chain, plot_scenario_tree
>>> T, _ = spring_packets.transition_matrix(4, 3, 0.035)
>>> print(A.shape, A.nnz)
(256, 256) 40960
>>> print("Scenarios in complete tree:", 256**5)
Scenarios in complete tree: 1099511627776
>>> tree_opts = {"depth": 5, "start_state": 255, "max_scenarios": 50}
>>> tree, cum_probs, _ = scenario_tree_from_markov_chain(A, **tree_opts)
>>> fmt = "Coverage of optimally pruned trees: {:.2f}% (1 scenario), {:.2f}% (50 scenarios)"
>>> print(fmt.format(100*cum_probs[0], 100*cum_probs[49]))
Coverage of optimally pruned trees: 10.01% (1 scenario), 40.99% (50 scenarios)
>>> plot_scenario_tree(tree)