Migrating from SciPy

If you are have been using SciPy to integrate ODEs, moving to numbakit-ode is very easy.

Migrating from SciPy class based API

Instantiating the solver class is mostly the same (except for the class name, see table below). So RK23(fun, t0, y0) becomes RungeKutta23(fun, t0, y0), RK45(fun, t0, y0) becomes RungeKutta45(fun, t0, y0), and so on. The step method available in the SciPy solver instance is also available in the numbakit-ode instance and has the same syntax (numbakit-ode’s step method provides a few extra parameters, but the defaults match the SciPy semantics)

SciPy	nbkode
RK23	RungeKutta23
RK45	RungeKutta45
DOP853	DOP853
BDF	BDF<N>*
Radau	N/A
LSODA	N/A

(*) We provide BDF, with N=1 to 5 N/A: not available (yet :-))

All extra parameters can be given as named arguments using the same name as in SciPy.

Migrating from SciPy solve_ivp

SciPy’s solve_ivp creates a Solver instance and steps through the solution until the desired time point. numbakit-ode takes a different approach: it provides a feature-rich solver class that you keep alive while you need it.

To run until a specific time:

>>> out = solve_ivp(exponential_decay, [0, 10], [2, 4, 8])
>>> print(out.t)
>>> print(out.y)

in numbakit-ode becomes:

>>> sol = nbkode.RungeKutta45(exponential_decay, 0, [2, 4, 8])
>>> t, y = sol.run(10)
>>> print(t)
>>> print(y)

Resuming the integration in SciPy involves calling solve_ivp again:

>>> out2 = solve_ivp(exponential_decay, [out.t, 20], out.y)
>>> print(out2.t)
>>> print(out2.y)

but bear in mind that for some solvers, this is not exactly the same as resuming as the internal state of the solver (which might contain previous evaluations of the function or jacobian) are lost.

That is why in numbakit-ode, we rather keep the solver alive and then call it again if necessary:

>>> t2, y = sol.run(10)
>>> print(t2)
>>> print(yt)

To evaluate at specific timepoints in SciPy:

>>> out = solve_ivp(exponential_decay, [0, 10], [2, 4, 8], t_eval=[0, 1, 2, 4, 10])

in numbakit-ode becomes:

>>> sol = nbkode.RungeKutta45(exponential_decay, 0, [2, 4, 8])
>>> t, y = sol.run([0, 1, 2, 4, 10])

To use events in SciPy:

>>> out = solve_ivp(upward_cannon, [0, 100], [0, 10], events=hit_ground)
>>> print(out.t_events)
>>> print(out.y_events)

in numbakit-ode becomes:

>>> sol = nbkode.RungeKutta45(exponential_decay, 0, [2, 4, 8])
>>> t, y, t_events, y_events = sol.run_events(100, events=hit_ground)
>>> print(t_events)
>>> print(y_events)

Keep in mind that in numbakit-ode, time always move forward.