def test_symplectic_against_undamped_harmonic_oscillator(self, stepper):
system = SymplecticUndampedSimpleHarmonicOscillatorSystem(
omega=1.0 * np.pi, init_val=np.array([0.2, 0.8]))
final_time = 4.0 * np.pi
n_steps = 2000
time_stepper = stepper()
integrate(time_stepper, system, final_time=final_time, n_steps=n_steps)
# Symplectic systems conserve energy to a certain extent
assert_allclose(
*system.compute_energy(final_time),
rtol=Tolerance.rtol() * 1e1,
atol=Tolerance.atol(),
)
def test_symplectic_steppers(self, symplectic_stepper):
collective_system = SymplecticUndampedHarmonicOscillatorCollectiveSystem(
)
final_time = 1.0
n_steps = 2000
stepper = symplectic_stepper()
integrate(stepper,
collective_system,
final_time=final_time,
n_steps=n_steps)
for system in collective_system:
assert_allclose(
*system.compute_energy(final_time),
rtol=Tolerance.rtol() * 1e1,
atol=Tolerance.atol(),
)
def test_symplectics_against_ellipse_motion(self, symplectic_stepper):
from elastica._elastica_numpy._systems._analytical import (
make_simple_system_with_positions_directors,
SimpleSystemWithPositionsDirectors,
)
random_start_position = np.random.randn(3, 1)
random_end_position = np.random.randn(3, 1)
random_directors, _ = np.linalg.qr(np.random.randn(3, 3))
random_directors = random_directors.reshape(3, 3, 1)
rod_like_system = make_simple_system_with_positions_directors(
random_start_position, random_end_position, random_directors)
final_time = 1.0
n_steps = 1000
stepper = symplectic_stepper()
integrate(stepper,
rod_like_system,
final_time=final_time,
n_steps=n_steps)
assert_allclose(
rod_like_system.position_collection,
rod_like_system.analytical_solution("Positions", final_time),
rtol=Tolerance.rtol() * 1e1,
atol=Tolerance.atol(),
)
assert_allclose(
rod_like_system.velocity_collection,
rod_like_system.analytical_solution("Velocity", final_time),
rtol=Tolerance.rtol() * 1e1,
atol=Tolerance.atol(),
)
# Reshaping done in the director collection to prevent numba from
# complaining about returning multiple types
assert_allclose(
rod_like_system.director_collection.reshape(-1, 1),
rod_like_system.analytical_solution("Directors", final_time),
rtol=Tolerance.rtol() * 1e1,
atol=Tolerance.atol(),
)
def test_integrate_throws_an_assert_for_negative_total_steps():
with pytest.raises(AssertionError) as excinfo:
integrate([], [], np.random.rand(1), -np.random.randint(100, 10000))
assert "steps is negative" in str(excinfo.value)
def test_integrate_throws_an_assert_for_negative_final_time():
with pytest.raises(AssertionError) as excinfo:
integrate([], [], -np.random.rand(1))
assert "time is negative" in str(excinfo.value)