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from math import fsum
import numpy as np
def is_near_equal(a, b, tol):
return np.allclose(a, b, rtol=0.0, atol=tol)
def run(mesh, volume, convol_norms, ce_ratio_norms, cellvol_norms, tol=1.0e-12):
# Check cell volumes.
total_cellvolume = fsum(mesh.cell_volumes)
assert abs(volume - total_cellvolume) < tol * volume, total_cellvolume
norm2 = np.linalg.norm(mesh.cell_volumes, ord=2)
norm_inf = np.linalg.norm(mesh.cell_volumes, ord=np.inf)
assert is_near_equal(cellvol_norms, [norm2, norm_inf], tol), [norm2, norm_inf]
# If everything is Delaunay and the boundary elements aren't flat, the volume of the
# domain is given by
# 1/n * edge_lengths * ce_ratios.
# Unfortunately, this isn't always the case.
# ```
# total_ce_ratio = \
# fsum(mesh.edge_lengths**2 * mesh.get_ce_ratios_per_edge() / dim)
# self.assertAlmostEqual(volume, total_ce_ratio, delta=tol * volume)
# ```
# Check ce_ratio norms.
alpha2 = fsum((mesh.ce_ratios**2).flat)
alpha_inf = max(abs(mesh.ce_ratios).flat)
assert is_near_equal(ce_ratio_norms, [alpha2, alpha_inf], tol), [alpha2, alpha_inf]
# Check the volume by summing over the absolute value of the control volumes.
vol = fsum(mesh.control_volumes)
assert abs(volume - vol) < tol * volume, vol
# Check control volume norms.
norm2 = np.linalg.norm(mesh.control_volumes, ord=2)
norm_inf = np.linalg.norm(mesh.control_volumes, ord=np.inf)
assert is_near_equal(convol_norms, [norm2, norm_inf], tol), [norm2, norm_inf]
def assert_norms(x, ref, tol):
ref = np.asarray(ref)
val = np.array(
[
np.linalg.norm(x.flat, 1),
np.linalg.norm(x.flat, 2),
np.linalg.norm(x.flat, np.inf),
]
)
assert np.all(np.abs(val - ref) < tol * np.abs(ref)), (
"Norms don't coincide.\n"
f"Expected: [{ref[0]:.16e}, {ref[1]:.16e}, {ref[2]:.16e}]\n"
f"Computed: [{val[0]:.16e}, {val[1]:.16e}, {val[2]:.16e}]\n"
)
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