mpsim

This is a python library for computing trajectories of Markov processes. Given a list of states and transition probabilities, mpsim computes sample sequences of states of either a fixed length or until an absorbing state is reached.

The library was created to generate many such trajectories efficiently and has a number of features such as caching of frequently needed intermediate computations, utilization of multiple processing cores, and callbacks for on-the-fly processing of trajectories.

Basic Usage

There are some examples included with the library, To use the library you need to supply a list of transitions in the following form:

[(source_state, target_state, transition_probability), ...]

The states of the process can be any hashable python object (integers, strings, etc.). These are compiled into a graph object representing the directed graph associated to the process.

For example:

    import mpsim
    edges = [('a', 'b', 0.5), ('a', 'a', 0.5), ('b', 'a', 0.8),
             ('b', 'b', 0.1), ('b', 'c', 0.1)]
    cache = mpsim.compile_edges(edges)
    random_seed, iterations, trajectory = mpsim.simulation(cache, initial_state='a')
    print "".join(trajectory)

This prints something like (depending on the random seed)

aaaaabababababaababababababaaaaaaabababaaaaaababaabc

The function mpsim.simulation accepts two additional keyword arguments:

• random_seed in case you want to specify the seed yourself, and
• max_iterations, in case you want to either limit the total iterations of the process or if you want trajectories of a particular length (if there are no absorbing states).

mpsim will detect absorbing states as those having no outbound edges or transitions.

Larger Scale Usage

The library was originally created to generate many long trajectories. For this usage case you likely want to take advantage of multiple processing cores and you will want to process the data on the fly to prevent the trajectories from accumulating in memory.

mpsim provides various helpers for this usage case in generators and callbacks. Let's look at a few of these in particular.

To limit memory usage, you can specify the number of trajectories to be generated in each batch (before passing to a callback). To do so, use mpsim.generators.iterations_generator as follows:

    mpsim.generators.iterations_generator(total, per_run=1000)

This will tell mpsim to generate total number of trajectories in batches of per_run, split over the available processing cores.

You also need to specify the initial state to use. This can be the same state every time, in which case you can use:

    initial_state_gen = mpsim.generators.constant_generator('a')

or a random state, in which case you could use:

    initial_state_gen = mpsim.generators.constant_generator(states)

Note that you must supply the states as a sequence, mpsim will not make any assumptions in this case as to what you may have wanted.

Finally you can specify a callback to process the trajectories in each batch. For example, perhaps you are only interested in the total length of the trajectories. The best way to do this is with a method of a class that keeps track of the lengths (this is in mpsim.callbacks):

    class LengthRecorder(object):
        """
        Records only length of trajectories.
        """

        def __init__(self):
            self.lengths = []

        def add(self, results):
            for seed, length, history in results:
                self.lengths.append(length)

Then you would pass the add method of an instance as the callback, like so:

    callback_obj = mpsim.callbacks.RunLengthRecorder()
    callback = callback_obj.add

mpsim will then pass the trajectories to the add function as each batch is generated. Note that this is done syncronyously at the end of each batch, not asynchronously as each trajectory is generated, so the callback does not need to be thread-safe but the processing does not utilize multiple cores. If you want to process on the fly with something thread-safe, you need to write a custom sim_func and pass it in as a keyword argument to batched_simulations (see simulations ).

Putting it all together:

    import mpsim
    from matplotlib import pyplot

    edges = [('a', 'b', 0.5), ('a', 'a', 0.5), ('b', 'a', 0.8),
                ('b', 'b', 0.1), ('b', 'c', 0.1)]
    cache = mpsim.compile_edges(edges)

    # Set up generators for batched processing
    initial_state_gen = mpsim.generators.constant_generator('a')
    parameter_gen = mpsim.generators.parameter_generator(cache, initial_state_gen)
    iters_gen = mpsim.generators.iterations_generator(100000)
    callback_obj = mpsim.callbacks.RunLengthRecorder()

    results = mpsim.batched_simulations(parameter_gen, iters_gen,
                                        callback=callback_obj.add)
    lengths = callback_obj.lengths

    # Plot the lengths as a histogram
    pyplot.hist(lengths, bins=30)
    pyplot.show()