def test_convert_constant_tensor(Nphi, Ntheta, Nr, k, dealias, basis, dtype):
c, d, b, phi, theta, r, x, y, z = basis(Nphi, Ntheta, Nr, k, dealias,
dtype)
f = field.Field(dist=d, dtype=dtype, tensorsig=(c, c))
f['g'][0, 0] = f['g'][1, 1] = f['g'][2, 2] = 1
g = operators.Convert(f, b).evaluate()
assert np.allclose(f['g'], g['g'])
def test_convert_constant_scalar(Nphi, Ntheta, Nr, k, dealias, basis, dtype):
c, d, b, phi, theta, r, x, y, z = basis(Nphi, Ntheta, Nr, k, dealias,
dtype)
f = field.Field(dist=d, dtype=dtype)
f['g'] = 1
g = operators.Convert(f, b).evaluate()
assert np.allclose(f['g'], g['g'])
def test_convert_constant_scalar_explicit(Nphi, Ntheta, dealias, dtype):
c, d, b, phi, theta = build_sphere(Nphi, Ntheta, dealias, dtype)
f = d.Field()
if np.iscomplexobj(dtype()):
fref = 1j
else:
fref = 1
f['g'] = fref
g = operators.Convert(f, b).evaluate()
assert np.allclose(g['g'], fref)
def test_jacobi_ncc_eval(N, a0, b0, k_ncc, k_arg, dealias, dtype):
"""
This tests for aliasing errors when evaluating the product
f(x) * g(x)
as both an NCC operator and with the pseudospectral method.
With 3/2 dealiasing, the product will generally contain aliasing
errors in the last 2*max(k_ncc, k_arg) modes. We can eliminate these
by zeroing the corresponding number of modes of f(x) and/or g(x).
"""
c = coords.Coordinate('x')
d = distributor.Distributor((c,))
b = basis.Jacobi(c, size=N, a=a0, b=b0, bounds=(0, 1), dealias=dealias)
b_ncc = b.clone_with(a=a0+k_ncc, b=b0+k_ncc)
b_arg = b.clone_with(a=a0+k_arg, b=b0+k_arg)
f = field.Field(dist=d, bases=(b_ncc,), dtype=dtype)
g = field.Field(dist=d, bases=(b_arg,), dtype=dtype)
f['g'] = np.random.randn(*f['g'].shape)
g['g'] = np.random.randn(*g['g'].shape)
x = b.local_grid(1)
f['g'] = np.cos(6*x)
g['g'] = np.cos(6*x)
kmax = max(k_ncc, k_arg)
if kmax > 0 and dealias < 2:
f['c'][-kmax:] = 0
g['c'][-kmax:] = 0
vars = [g]
w0 = f * g
w1 = w0.reinitialize(ncc=True, ncc_vars=vars)
problem = problems.LBVP(vars)
problem.add_equation((w1, 0))
solver = solvers.LinearBoundaryValueSolver(problem)
w1.store_ncc_matrices(vars, solver.subproblems)
w0 = w0.evaluate()
w2 = field.Field(dist=d, bases=(b,), dtype=dtype)
w2.preset_scales(w2.domain.dealias)
w2['g'] = w0['g']
w2['c']
w0['c']
print(np.max(np.abs(w2['g'] - w0['g'])))
w2 = operators.Convert(w2, w0.domain.bases[0]).evaluate()
w1 = w1.evaluate_as_ncc()
assert np.allclose(w0['c'], w2['c'])