def test_jac_simpl():
model = Model("dxxU", "U")
model_simp = Model("dxxU", "U", simplify=True)
x = np.linspace(0, 2 * np.pi, 50, endpoint=False)
U = np.cos(x)
assert np.isclose(
model.J(model.fields_template(x=x, U=U),
dict(periodic=True)).todense(),
model.J(model_simp.fields_template(x=x, U=U),
dict(periodic=True)).todense(),
).all()
def test_model_monovariate(func, var, par, k, compiler):
model = Model(func, var, par, compiler=compiler)
x, dx = np.linspace(0, 10, 100, retstep=True, endpoint=False)
U = np.cos(x * 2 * np.pi / 10)
fields = model.fields_template(x=x, U=U)
parameters = dict(periodic=True, k=k)
F = model.F(fields, parameters)
J_sparse = model.J(fields, parameters)
J_dense = model.J(fields, parameters, sparse=False)
J_approx = model.F.diff_approx(fields, parameters)
dxU = np.gradient(np.pad(U, 2, mode="wrap")) / dx
dxxU = np.gradient(dxU) / dx
dxU = dxU[2:-2]
dxxU = dxxU[2:-2]
assert np.isclose(F, k * dxxU, rtol=1E-2).all()
assert np.isclose(J_approx, J_sparse.todense(), rtol=1E-2).all()
assert np.isclose(J_approx, J_dense, rtol=1E-2).all()
def test_model_bivariate():
model = Model(["k1 * dxx(v)", "k2 * dxx(u)"], ["u", "v"], ["k1", "k2"])
x, dx = np.linspace(0, 10, 50, retstep=True, endpoint=False)
u = np.cos(x * 2 * np.pi / 10)
v = np.sin(x * 2 * np.pi / 10)
fields = model.fields_template(x=x, u=u, v=v)
parameters = dict(periodic=True, k1=1, k2=1)
F = model.F(fields, parameters)
J_sparse = model.J(fields, parameters)
J_dense = model.J(fields, parameters, sparse=False)
J_approx = model.F.diff_approx(fields, parameters, eps=1E-3)
dxu = np.gradient(np.pad(u, 2, mode="wrap")) / dx
dxxu = np.gradient(dxu) / dx
dxu = dxu[2:-2]
dxxu = dxxu[2:-2]
dxv = np.gradient(np.pad(v, 2, mode="wrap")) / dx
dxxv = np.gradient(dxv) / dx
dxv = dxv[2:-2]
dxxv = dxxv[2:-2]
assert np.isclose(F, np.vstack([dxxv, dxxu]).flatten("F"), rtol=1E-2).all()
assert np.isclose(J_approx, J_sparse.todense(), rtol=1E-4).all()
assert np.isclose(J_approx, J_dense, rtol=1E-4).all()
def test_upwind(compiler, uporder, vel, periodic):
model = Model(
differential_equations=["upwind(%s, U, %i)" % (vel, uporder)],
dependent_variables="U",
parameters="k",
help_functions="s",
compiler=compiler,
)
x, dx = np.linspace(0, 10, 100, retstep=True, endpoint=False)
U = np.cos(x * 2 * np.pi / 10)
s = np.zeros_like(x)
fields = model.fields_template(x=x, U=U, s=s)
parameters = dict(periodic=periodic, k=1)
model.F(fields, parameters)
model.J(fields, parameters)
def test_model_api(compiler, periodic):
model = Model(
differential_equations=["k * dxxU + s"],
dependent_variables="U",
parameters="k",
help_functions="s",
compiler=compiler,
)
assert set(model._args) == set(
["x", "U_m1", "U", "U_p1", "s_m1", "s", "s_p1", "k", "dx"])
with pytest.raises(NotImplementedError):
Model("dxxxxxU", "U")
with pytest.raises(ValueError):
Model("dxxx(dx)", "U")
x, dx = np.linspace(0, 10, 100, retstep=True, endpoint=False)
U = np.cos(x * 2 * np.pi / 10)
s = np.zeros_like(x)
fields = model.fields_template(x=x, U=U, s=s)
parameters = dict(periodic=periodic, k=1)
model.F(fields, parameters)
model.J(fields, parameters)