def test_diffuse_centered_batched(self):
grid = CenteredGrid(Noise(batch=2, vector=2),
extrapolation.PERIODIC,
x=4,
y=3)
diffuse.explicit(grid, 1, 1, substeps=10)
diffuse.implicit(grid, 1, 1, order=2)
diffuse.fourier(grid, 1, 1)
def test_consistency_implicit(self):
DOMAIN = Domain(x=200, boundaries=PERIODIC)
DIFFUSIVITY = 0.5
grid = DOMAIN.scalar_grid((1,) * 100 + (0,) * 100)
for extrap in (extrapolation.ZERO, extrapolation.BOUNDARY, extrapolation.PERIODIC):
grid = grid.with_(extrapolation=extrap)
implicit = diffuse.implicit(grid, DIFFUSIVITY, 1, order=10)
back_implicit = diffuse.implicit(implicit, DIFFUSIVITY, -1, order=10)
field.assert_close(grid, back_implicit, rel_tolerance=0, abs_tolerance=0.1)
def test_constant_diffusion(self):
DOMAIN = Domain(x=4, y=3, boundaries=PERIODIC)
grid = DOMAIN.scalar_grid(1)
explicit = diffuse.explicit(grid, 1, 1, substeps=10)
implicit = diffuse.implicit(grid, 1, 1, order=2)
fourier = diffuse.fourier(grid, 1, 1)
math.assert_close(grid.values, explicit.values, implicit.values, fourier.values)
def test_constant_diffusion(self):
grid = CenteredGrid(1, extrapolation.PERIODIC, x=4, y=3)
explicit = diffuse.explicit(grid, 1, 1, substeps=10)
implicit = diffuse.implicit(grid, 1, 1, order=2)
fourier = diffuse.fourier(grid, 1, 1)
math.assert_close(grid.values, explicit.values, implicit.values,
fourier.values)
def test_consistency_implicit(self):
DIFFUSIVITY = 0.5
grid = CenteredGrid((1, ) * 100 + (0, ) * 100,
extrapolation.PERIODIC,
x=200)
for extrap in (extrapolation.ZERO, extrapolation.BOUNDARY,
extrapolation.PERIODIC):
grid = grid.with_extrapolation(extrap)
implicit = diffuse.implicit(grid, DIFFUSIVITY, 1, order=10)
back_implicit = diffuse.implicit(implicit,
DIFFUSIVITY,
-1,
order=10)
field.assert_close(grid,
back_implicit,
rel_tolerance=0,
abs_tolerance=0.1)
def test_implicit_stability(self):
DIFFUSIVITY = 10
grid = CenteredGrid((1, ) * 3 + (0, ) * 3, extrapolation.PERIODIC, x=6)
try:
implicit = diffuse.implicit(grid, DIFFUSIVITY, 1, order=10)
print(implicit.values)
field.assert_close(0 <= implicit <= 1.0001, True)
except NotConverged as err:
print(err)
pass # solve_linear did not converge
def test_implicit_stability(self):
DOMAIN = Domain(x=6, boundaries=PERIODIC)
DIFFUSIVITY = 10
grid = DOMAIN.scalar_grid((1,) * 3 + (0,) * 3)
try:
implicit = diffuse.implicit(grid, DIFFUSIVITY, 1, order=10)
print(implicit.values)
field.assert_close(0 <= implicit <= 1.0001, True)
except AssertionError as err:
print(err)
pass # solve did not converge
def test_equality_1d_periodic(self):
DOMAIN = Domain(x=200, boundaries=PERIODIC)
DIFFUSIVITY = 0.5
grid = DOMAIN.scalar_grid((1,) * 100 + (0,) * 100)
explicit = diffuse.explicit(grid, DIFFUSIVITY, 1, substeps=1000)
implicit = diffuse.implicit(grid, DIFFUSIVITY, 1, order=10)
fourier = diffuse.fourier(grid, DIFFUSIVITY, 1)
field.assert_close(explicit, implicit, rel_tolerance=0, abs_tolerance=0.01)
field.assert_close(explicit, implicit, fourier, rel_tolerance=0, abs_tolerance=0.1)
# print(f"{explicit.values[:6]} Explicit")
# print(f"{implicit.values[:6]} Implicit")
# print(f"{fourier.values[:6]} Fourier")
# print()
back_explicit = diffuse.explicit(explicit, DIFFUSIVITY, -1, substeps=1000)
back_implicit = diffuse.implicit(implicit, DIFFUSIVITY, -1, order=10)
back_fourier = diffuse.fourier(fourier, DIFFUSIVITY, -1)
# print(f"{back_explicit.values[:6]} Explicit")
# print(f"{back_implicit.values[:6]} Implicit")
# print(f"{back_fourier.values[:6]} Fourier")
field.assert_close(grid, back_explicit, back_implicit, back_fourier, rel_tolerance=0, abs_tolerance=0.1)
def test_diffuse_staggered_batched(self):
for diffusivity in [1, 0.5, math.wrap([1., 0.5], batch('batch'))]:
grid = StaggeredGrid(Noise(batch(batch=2), vector=2),
extrapolation.PERIODIC,
x=4,
y=3)
diffuse.explicit(grid, diffusivity, 1, substeps=10)
diffuse.implicit(grid, diffusivity, 1, order=2)
diffuse.fourier(grid, diffusivity, 1)
grid = StaggeredGrid(Noise(batch(batch=2), vector=2),
extrapolation.ZERO,
x=4,
y=3)
diffuse.explicit(grid, diffusivity, 1, substeps=10)
# diffuse.implicit(grid, diffusivity, 1, order=2) # not yet supported
grid = StaggeredGrid(Noise(batch(batch=2), vector=2),
extrapolation.BOUNDARY,
x=4,
y=3)
diffuse.explicit(grid, diffusivity, 1, substeps=10)
def test_equality_1d_periodic(self):
DIFFUSIVITY = 0.5
grid = CenteredGrid((1, ) * 100 + (0, ) * 100,
extrapolation.PERIODIC,
x=200)
explicit = diffuse.explicit(grid, DIFFUSIVITY, 1, substeps=1000)
implicit = diffuse.implicit(grid, DIFFUSIVITY, 1, order=10)
fourier = diffuse.fourier(grid, DIFFUSIVITY, 1)
field.assert_close(explicit,
implicit,
rel_tolerance=0,
abs_tolerance=0.01)
field.assert_close(explicit,
implicit,
fourier,
rel_tolerance=0,
abs_tolerance=0.1)
# print(f"{explicit.values[:6]} Explicit")
# print(f"{implicit.values[:6]} Implicit")
# print(f"{fourier.values[:6]} Fourier")
# print()
back_explicit = diffuse.explicit(explicit,
DIFFUSIVITY,
-1,
substeps=1000)
back_implicit = diffuse.implicit(implicit, DIFFUSIVITY, -1, order=10)
back_fourier = diffuse.fourier(fourier, DIFFUSIVITY, -1)
# print(f"{back_explicit.values[:6]} Explicit")
# print(f"{back_implicit.values[:6]} Implicit")
# print(f"{back_fourier.values[:6]} Fourier")
field.assert_close(grid,
back_explicit,
back_implicit,
back_fourier,
rel_tolerance=0,
abs_tolerance=0.1)