"""ODE solver interface."""
from abc import ABC, abstractmethod
class ODESolver(ABC):
"""Interface for ODESolver."""
def __init__(self, ivp, order):
self.ivp = ivp
self.order = order # e.g.: RK45 has order=5, IBM(q) has order=q
self.num_steps = 0
[docs] def solve(self, steprule):
"""Solve an IVP.
Parameters
----------
steprule : :class:`StepRule`
Step-size selection rule, e.g. constant steps or adaptive steps.
"""
t, current_rv = self.initialise()
times, rvs = [t], [current_rv]
stepsize = steprule.firststep
while t < self.ivp.tmax:
t_new = t + stepsize
proposed_rv, errorest = self.step(t, t_new, current_rv)
internal_norm = steprule.errorest_to_norm(
errorest=errorest,
proposed_state=proposed_rv.mean,
current_state=current_rv.mean,
)
if steprule.is_accepted(internal_norm):
self.num_steps += 1
self.method_callback(
time=t_new, current_guess=proposed_rv, current_error=errorest
)
t = t_new
current_rv = proposed_rv
times.append(t)
rvs.append(current_rv)
suggested_stepsize = steprule.suggest(
stepsize, internal_norm, localconvrate=self.order + 1
)
stepsize = min(suggested_stepsize, self.ivp.tmax - t)
odesol = self.rvlist_to_odesol(times=times, rvs=rvs)
odesol = self.postprocess(odesol)
return odesol
[docs] @abstractmethod
def initialise(self):
"""Returns t0 and y0 (for the solver, which might be different to ivp.y0)"""
raise NotImplementedError
[docs] @abstractmethod
def step(self, start, stop, current, **kwargs):
"""Every ODE solver needs a step() method that returns a new random variable and
an error estimate."""
raise NotImplementedError
[docs] @abstractmethod
def rvlist_to_odesol(self, times, rvs):
"""Create an ODESolution object."""
raise NotImplementedError
[docs] def postprocess(self, odesol):
"""Process the ODESolution object before returning."""
return odesol
[docs] def method_callback(self, time, current_guess, current_error):
"""Optional callback.
Can be overwritten. Do this as soon as it is clear that the
current guess is accepted, but before storing it. No return. For
example: tune hyperparameters (sigma).
"""
pass