def load_lotkavolterra():
"""Load LV system as a basic IVP."""
y0 = np.array([20, 20])
return diffeq_zoo.lotkavolterra(t0=0.0,
tmax=0.55,
y0=y0,
params=(0.5, 0.05, 0.5, 0.05))
def posterior(stepsize, timespan):
"""Kalman smoothing posterior."""
t0, tmax = timespan
y0 = 20 * np.ones(2)
ivp = diffeq_zoo.lotkavolterra(t0=t0, tmax=tmax, y0=y0)
f = ivp.f
t0, tmax = ivp.t0, ivp.tmax
return diffeq.probsolve_ivp(f, t0, tmax, y0, step=stepsize, adaptive=False)
def perturbed_solution(steprule):
y0 = np.array([0.1, 0.1])
ode = diffeq_zoo.lotkavolterra(t0=0.0, tmax=1.0, y0=y0)
rng = np.random.default_rng(seed=1)
testsolver = diffeq.perturbed.scipy_wrapper.WrappedScipyRungeKutta(
rk.RK45, steprule=steprule)
sol = diffeq.perturbed.step.PerturbedStepSolver(
rng=rng,
solver=testsolver,
noise_scale=0.1,
perturb_function=diffeq.perturbed.step.perturb_uniform,
)
return sol.solve(ode)
def ivp():
y0 = 20.0 * np.ones(2)
return diffeq_zoo.lotkavolterra(t0=0.0, tmax=0.25, y0=y0)
def case_lotkavolterra(perturbfun, steprule):
y0 = np.array([0.1, 0.1])
ode = diffeq_zoo.lotkavolterra(t0=0.0, tmax=1.0, y0=y0)
return setup_solver(y0, ode, perturbfun, steprule=steprule)
def problem_lotka_volterra():
ivp = diffeq_zoo.lotkavolterra()
inits_matrix_full = known_initial_derivatives.LV_INITS
return ivp, inits_matrix_full
@pytest.fixture
def locations():
return np.linspace(0.0, 1.0, 20)
@pytest.fixture
def ode_information_operator():
op = diffeq.odefilter.information_operators.ODEResidual(
num_prior_derivatives=3, ode_dimension=2)
return op
@pytest.mark.parametrize(
"ivp", [diffeq_zoo.lotkavolterra(),
diffeq_zoo.fitzhughnagumo()])
@pytest.mark.parametrize("ode_measurement_variance", [0.0, 1.0])
@pytest.mark.parametrize("exclude_initial_condition", [True, False])
@pytest.mark.parametrize(
"approx_strategy",
[
None,
diffeq.odefilter.approx_strategies.EK0(),
diffeq.odefilter.approx_strategies.EK1(),
],
)
def test_ivp_to_regression_problem(
ivp,
locations,
ode_information_operator,
import numpy as np
import pytest
import probnum.problems as pnpr
import probnum.problems.zoo.diffeq as diffeqzoo
ODE_LIST = [
diffeqzoo.vanderpol(),
diffeqzoo.threebody(),
diffeqzoo.rigidbody(),
diffeqzoo.lotkavolterra(),
diffeqzoo.logistic(),
diffeqzoo.seir(),
diffeqzoo.fitzhughnagumo(),
diffeqzoo.lorenz63(),
diffeqzoo.lorenz96(),
]
all_odes = pytest.mark.parametrize("ivp", ODE_LIST)
@all_odes
def test_isinstance(ivp):
assert isinstance(ivp, pnpr.InitialValueProblem)
@all_odes
def test_eval(ivp):
f0 = ivp.f(ivp.t0, ivp.y0)
assert isinstance(f0, np.ndarray)
if ivp.df is not None:
@pytest.fixture
def locations():
return np.linspace(0.0, 1.0, 20)
@pytest.fixture
def ode_information_operator():
op = diffeq.odefilter.information_operators.ODEResidual(
num_prior_derivatives=3, ode_dimension=2
)
return op
@pytest.mark.parametrize(
"ivp", [diffeq_zoo.lotkavolterra(), diffeq_zoo.fitzhughnagumo()]
)
@pytest.mark.parametrize("ode_measurement_variance", [0.0, 1.0])
@pytest.mark.parametrize("exclude_initial_condition", [True, False])
@pytest.mark.parametrize(
"approx_strategy",
[
None,
diffeq.odefilter.approx_strategies.EK0(),
diffeq.odefilter.approx_strategies.EK1(),
],
)
def test_ivp_to_regression_problem(
ivp,
locations,
ode_information_operator,
def lotka_volterra():
y0 = np.array([20.0, 20.0])
# tmax is ignored anyway
return diffeq_zoo.lotkavolterra(t0=0.0, tmax=np.inf, y0=y0)