stochastic-arrow 0.0.1

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arrow

“... even if the previous millisecond is closer to us than the birth of the universe, it is equally out of reach.” ― Jean-Christophe Valtat, Luminous Chaos

concept

This library implements a generalized version of the Gillespie Algorithm, a stochastic approach to numerically solving discrete systems. Each iteration, the algorithm will calculate the propensities for each reaction given a rate and the counts of the reactants present in the current state of the system, then selects one reaction to occur and the interval of time between the previous reaction and the current reaction. Iterating this produces a trajectory (or history) of the state vector over the course of the simulation.

usage

The arrow library presents a single class as an interface, StochasticSystem, which operates on a set of reactions (encoded as a numpy matrix) and associated reaction rates:

from arrow import StochasticSystem
import numpy as np

# Each row is a reaction and each column is a molecular species (or other entity).
# The top reaction here means that the first and second elements combine to create the third,
# while the fourth is unaffected.
reactions = np.array([
    [-1, -1, 1, 0],
    [-2, 0, 0, 1],
    [1, 1, -1, 0]])

# Each reaction has an associated rate for how probable that reaction is.
rates = np.array([3, 1, 1])

# Once we have a matrix of reactions and their associated rates, we can construct the system.
system = StochasticSystem(reactions, rates)

Now that the system has been instantiated, we can invoke it with any initial state vector and then run it for a given time interval:

# This gives the initial state of the system (counts of each molecular species, for instance)
state = np.array([1000, 1000, 0, 0])

# We also specify how long we want the simulation to run. Here we set it to one second
duration = 1

# Once we have an initial state and duration, we can run the simulation for the given duration.
# `evolve` returns the history of the state vector for each time step, and the history of time
# steps as they will be in uneven increments throughout the simulation.
history, steps = system.evolve(state, duration)