def test_padding_biharmonic(family):
N = 8
B = FunctionSpace(N, family, bc=(0, 0, 0, 0))
Bp = B.get_dealiased(1.5)
u = Function(B)
u[:(N - 4)] = np.random.random(N - 4)
up = Array(Bp)
up = Bp.backward(u, fast_transform=False)
uf = Bp.forward(up, fast_transform=False)
assert np.linalg.norm(uf - u) < 1e-12
if family == 'C':
up = Bp.backward(u)
uf = Bp.forward(up)
assert np.linalg.norm(uf - u) < 1e-12
# Test padding 2D
F = FunctionSpace(N, 'F', dtype='d')
T = TensorProductSpace(comm, (B, F))
Tp = T.get_dealiased(1.5)
u = Function(T)
u[:-4, :-1] = np.random.random(u[:-4, :-1].shape)
up = Tp.backward(u)
uc = Tp.forward(up)
assert np.linalg.norm(u - uc) < 1e-8
# Test padding 3D
F1 = FunctionSpace(N, 'F', dtype='D')
T = TensorProductSpace(comm, (F1, F, B))
Tp = T.get_dealiased(1.5)
u = Function(T)
u[:, :, :-4] = np.random.random(u[:, :, :-4].shape)
u = u.backward().forward() # Clean
up = Tp.backward(u)
uc = Tp.forward(up)
assert np.linalg.norm(u - uc) < 1e-8
def test_padding_neumann(family):
N = 8
B = FunctionSpace(N, family, bc={'left': ('N', 0), 'right': ('N', 0)})
Bp = B.get_dealiased(1.5)
u = Function(B)
u[1:-2] = np.random.random(N - 3)
up = Array(Bp)
up = Bp.backward(u, fast_transform=False)
uf = Bp.forward(up, fast_transform=False)
assert np.linalg.norm(uf - u) < 1e-12
if family == 'C':
up = Bp.backward(u)
uf = Bp.forward(up)
assert np.linalg.norm(uf - u) < 1e-12
# Test padding 2D
F = FunctionSpace(N, 'F', dtype='d')
T = TensorProductSpace(comm, (B, F))
Tp = T.get_dealiased(1.5)
u = Function(T)
u[1:-2, :-1] = np.random.random(u[1:-2, :-1].shape)
up = Tp.backward(u)
uc = Tp.forward(up)
assert np.linalg.norm(u - uc) < 1e-8
# Test padding 3D
F1 = FunctionSpace(N, 'F', dtype='D')
T = TensorProductSpace(comm, (F1, F, B))
Tp = T.get_dealiased(1.5)
u = Function(T)
u[:, :, 1:-2] = np.random.random(u[:, :, 1:-2].shape)
u = u.backward().forward() # Clean
up = Tp.backward(u)
uc = Tp.forward(up)
assert np.linalg.norm(u - uc) < 1e-8
def test_padding_orthogonal(family):
N = 8
B = FunctionSpace(N, family)
Bp = B.get_dealiased(1.5)
u = Function(B)
u[:] = np.random.random(u.shape)
up = Array(Bp)
if family != 'F':
up = Bp.backward(u, fast_transform=False)
uf = Bp.forward(up, fast_transform=False)
assert np.linalg.norm(uf - u) < 1e-12
if family in ('C', 'F'):
up = Bp.backward(u, fast_transform=True)
uf = Bp.forward(up, fast_transform=True)
assert np.linalg.norm(uf - u) < 1e-12
# Test padding 2D
dtype = 'D' if family == 'F' else 'd'
F = FunctionSpace(N, 'F', dtype=dtype)
T = TensorProductSpace(comm, (F, B))
Tp = T.get_dealiased(1.5)
u = Function(T)
u[:] = np.random.random(u.shape)
u = u.backward().forward()
up = Tp.backward(u)
uc = Tp.forward(up)
assert np.linalg.norm(u - uc) < 1e-8
# Test padding 3D
F1 = FunctionSpace(N, 'F', dtype='D')
T = TensorProductSpace(comm, (F1, F, B))
Tp = T.get_dealiased(1.5)
u = Function(T)
u[:] = np.random.random(u.shape)
u = u.backward().forward() # Clean
up = Tp.backward(u)
uc = Tp.forward(up)
assert np.linalg.norm(u - uc) < 1e-8
def test_padding(family):
N = 8
B = FunctionSpace(N, family, bc=(-1, 1), domain=(-2, 2))
Bp = B.get_dealiased(1.5)
u = Function(B).set_boundary_dofs()
#u[:(N-2)] = np.random.random(N-2)
u[:(N - 2)] = 1
up = Array(Bp)
up = Bp.backward(u, fast_transform=False)
uf = Bp.forward(up, fast_transform=False)
assert np.linalg.norm(uf - u) < 1e-12
if family == 'C':
up = Bp.backward(u)
uf = Bp.forward(up)
assert np.linalg.norm(uf - u) < 1e-12
# Test padding 2D
F = FunctionSpace(N, 'F', dtype='d')
T = TensorProductSpace(comm, (B, F))
Tp = T.get_dealiased(1.5)
u = Function(T).set_boundary_dofs()
u[:-2, :-1] = np.random.random(u[:-2, :-1].shape)
up = Tp.backward(u)
uc = Tp.forward(up)
assert np.linalg.norm(u - uc) < 1e-8
# Test padding 3D
F1 = FunctionSpace(N, 'F', dtype='D')
T = TensorProductSpace(comm, (F1, F, B))
Tp = T.get_dealiased(1.5)
u = Function(T).set_boundary_dofs()
u[:, :, :-2] = np.random.random(u[:, :, :-2].shape)
u = u.backward().forward() # Clean
up = Tp.backward(u)
uc = Tp.forward(up)
assert np.linalg.norm(u - uc) < 1e-8
