def test_reconstruction_symmetry(self, u):
u = np.array(u, dtype=float)
def flip(x):
return x[::-1]
def flip_staggered(x):
return flip(np.roll(x, +1))
left_direct = weno.reconstruct_left(u)
left_flipped = flip_staggered(weno.reconstruct_right(flip(u)))
np.testing.assert_allclose(left_direct, left_flipped, atol=1e-6)
right_direct = weno.reconstruct_right(u)
right_flipped = flip_staggered(weno.reconstruct_left(flip(u)))
np.testing.assert_allclose(right_direct, right_flipped, atol=1e-6)
def test_batched(self):
u_batched = np.array([[0, 0, 0, 1, 2, 3, 4], [0, 0, 1, 2, 3, 4, 5]])
expected_left = np.stack([
weno.reconstruct_left(u_batched[0]),
weno.reconstruct_left(u_batched[1])
])
expected_right = np.stack([
weno.reconstruct_right(u_batched[0]),
weno.reconstruct_right(u_batched[1])
])
actual_left = weno.reconstruct_left(u_batched)
actual_right = weno.reconstruct_right(u_batched)
np.testing.assert_allclose(actual_left, expected_left)
np.testing.assert_allclose(actual_right, expected_right)
def __call__(self, t: float, y: np.ndarray) -> np.ndarray: space_derivatives = self.poly_diff.calculate_space_derivatives(y) # replace u^- and u^+ with WENO reconstructions assert 'u_minus' in space_derivatives and 'u_plus' in space_derivatives space_derivatives['u_minus'] = np.roll(weno.reconstruct_left(y), 1) space_derivatives['u_plus'] = np.roll(weno.reconstruct_right(y), 1) time_derivative = self.equation.equation_of_motion(y, space_derivatives) return self.equation.finalize_time_derivative(t, time_derivative)
def baseline_space_derivatives(inputs: tf.Tensor,
equation: equations.Equation,
accuracy_order: int = None) -> tf.Tensor:
"""Calculate spatial derivatives using a baseline metohd."""
assert_consistent_solution(equation, inputs)
spatial_derivatives_list = []
for derivative_name, derivative_order in zip(equation.DERIVATIVE_NAMES,
equation.DERIVATIVE_ORDERS):
if accuracy_order is None:
# use the best baseline method
assert equation.exact_type() is type(equation)
if equation.EXACT_METHOD is equations.ExactMethod.POLYNOMIAL:
grid = (0.5 + np.arange(-3, 3)) * equation.grid.solution_dx
method = FINITE_VOL if equation.CONSERVATIVE else FINITE_DIFF
derivative = polynomials.reconstruct(inputs, grid, method,
derivative_order)
elif equation.EXACT_METHOD is equations.ExactMethod.SPECTRAL:
derivative = duckarray.spectral_derivative(
inputs, derivative_order, equation.grid.period)
elif equation.EXACT_METHOD is equations.ExactMethod.WENO:
if derivative_name == 'u_minus':
derivative = duckarray.roll(weno.reconstruct_left(inputs),
1,
axis=-1)
elif derivative_name == 'u_plus':
derivative = duckarray.roll(weno.reconstruct_right(inputs),
1,
axis=-1)
else:
assert derivative_name == 'u_x'
grid = polynomials.regular_grid(
grid_offset=equation.GRID_OFFSET,
derivative_order=derivative_order,
accuracy_order=3,
dx=equation.grid.solution_dx)
method = FINITE_VOL if equation.CONSERVATIVE else FINITE_DIFF
derivative = polynomials.reconstruct(
inputs, grid, method, derivative_order)
else:
# explicit accuracy order provided
assert type(equation) not in equations.FLUX_EQUATION_TYPES
grid = polynomials.regular_grid(grid_offset=equation.GRID_OFFSET,
derivative_order=derivative_order,
accuracy_order=accuracy_order,
dx=equation.grid.solution_dx)
method = FINITE_VOL if equation.CONSERVATIVE else FINITE_DIFF
derivative = polynomials.reconstruct(inputs, grid, method,
derivative_order)
spatial_derivatives_list.append(derivative)
return tf.stack(spatial_derivatives_list, axis=-1)
def test_reconstruct_right_discontinuity(self): u = np.array([0, 1, 2, 3, 4, -4, -3, -2, -1]) actual = weno.reconstruct_right(u) expected = [0.5, 1.5, 2.5, 3.5, -4.5, -3.5, -2.5, -1.5, -0.5] np.testing.assert_allclose(actual, expected, atol=0.005)