def test_laplace_cyl():
""" test the implementation of the laplace operator """
for boundary_z in ["periodic", "derivative"]:
grid = CylindricalGrid(4, (0, 5), (8, 16),
periodic_z=(boundary_z == "periodic"))
a_2d = np.random.uniform(0, 1, grid.shape)
bcs = grid.get_boundary_conditions(["derivative", boundary_z])
lap_2d = ops.make_laplace(bcs)
b_2d = lap_2d(a_2d)
assert b_2d.shape == grid.shape
def main():
""" main routine testing the performance """
print("Reports calls-per-second (larger is better)")
print(" The `CUSTOM` method implemented by hand is the baseline case.")
print(
" The `FLEXIBLE` method is a serial implementation using the "
"boundary conditions from the package."
)
print(" The other methods use the functions supplied by the package.\n")
# Cartesian grid with different shapes and boundary conditions
for shape in [(32, 32), (512, 512)]:
data = np.random.random(shape)
for periodic in [True, False]:
grid = UnitGrid(shape, periodic=periodic)
bcs = Boundaries.from_data(grid, "natural")
print(grid)
result = cartesian.make_laplace(bcs, method="scipy")(data)
for method in ["FLEXIBLE", "CUSTOM", "numba", "matrix", "scipy"]:
if method == "FLEXIBLE":
laplace = flexible_laplace_2d(bcs)
elif method == "CUSTOM":
laplace = custom_laplace_2d(shape, periodic=periodic)
elif method in {"numba", "matrix", "scipy"}:
laplace = cartesian.make_laplace(bcs, method=method)
else:
raise ValueError(f"Unknown method `{method}`")
# call once to pre-compile and test result
np.testing.assert_allclose(laplace(data), result)
speed = estimate_computation_speed(laplace, data)
print(f"{method:>8s}: {int(speed):>9d}")
print()
# Cylindrical grid with different shapes
for shape in [(32, 64), (512, 512)]:
data = np.random.random(shape)
grid = CylindricalGrid(shape[0], [0, shape[1]], shape)
print(f"Cylindrical grid, shape={shape}")
bcs = Boundaries.from_data(grid, "no-flux")
laplace_cyl = cylindrical.make_laplace(bcs)
result = laplace_cyl(data)
for method in ["CUSTOM", "numba"]:
if method == "CUSTOM":
laplace = custom_laplace_cyl_no_flux(shape)
elif method == "numba":
laplace = laplace_cyl
else:
raise ValueError(f"Unknown method `{method}`")
# call once to pre-compile and test result
np.testing.assert_allclose(laplace(data), result)
speed = estimate_computation_speed(laplace, data)
print(f"{method:>8s}: {int(speed):>9d}")
print()
# Spherical grid with different shapes
for shape in [32, 512]:
data = np.random.random(shape)
grid = SphericalGrid(shape, shape)
print(grid)
bcs = Boundaries.from_data(grid, "no-flux")
make_laplace = spherical.make_laplace
for conservative in [True, False]:
laplace = make_laplace(bcs, conservative=conservative)
# call once to pre-compile
laplace(data)
speed = estimate_computation_speed(laplace, data)
print(f" numba (conservative={str(conservative):<5}): {int(speed):>9d}")
print()