def test_identity(self):
x = np.linspace(-1, 1, 100)
u = x**2
identity = Identity()
assert_array_equal(u, identity(u))
twice_id = Coef(2) * Identity()
assert_array_equal(2 * u, twice_id(u))
x_id = Coef(x) * Identity()
assert_array_equal(x * u, x_id(u))
def test_identity_2d(self):
(X, Y), (x, y), _ = grid(2, 100, -1, 1)
u = X**2 + Y**2
identity = Identity()
assert_array_equal(u, identity(u))
twice_id = Coef(2) * Identity()
assert_array_equal(2 * u, twice_id(u))
x_id = Coef(X) * Identity()
assert_array_equal(X * u, x_id(u))
dx = x[1] - x[0]
d_dx = FinDiff(0, dx)
linop = d_dx + 2 * Identity()
assert_array_almost_equal(2 * X + 2 * u, linop(u))
def test_1d_oscillator_free_dirichlet(self):
n = 300
shape = n,
t = np.linspace(0, 5, n)
dt = t[1] - t[0]
L = FinDiff(0, dt, 2) + Identity()
bc = BoundaryConditions(shape)
bc[0] = 1
bc[-1] = 2
eq = PDE(L, np.zeros_like(t), bc)
u = eq.solve()
expected = np.cos(t) - (np.cos(5) - 2) * np.sin(t) / np.sin(5)
np.testing.assert_array_almost_equal(expected, u, decimal=4)
def test_1d_oscillator_driv_neumann(self):
n = 200
shape = n,
t = np.linspace(0, 1, n)
dt = t[1] - t[0]
L = FinDiff(0, dt, 2) - FinDiff(0, dt) + Identity()
f = -3 * np.exp(-t) * np.cos(t) + 2 * np.exp(-t) * np.sin(t)
expected = np.exp(-t) * np.sin(t)
bc = BoundaryConditions(shape)
bc[0] = FinDiff(0, dt), 1
bc[-1] = expected[-1]
eq = PDE(L, f, bc)
u = eq.solve()
np.testing.assert_array_almost_equal(expected, u, decimal=4)
def test_eigs(self):
shape = 8,
x = np.linspace(-10, 10, shape[0])
dx = x[1] - x[0]
hbar = 1
m = 1
omega = 1
T = Coef(-hbar**2 / (2 * m)) * FinDiff(0, dx, 2)
V = Coef(0.5 * omega * x**2) * Identity()
H = T + V
print("\n", T.matrix(shape).toarray())
print("\n", V.matrix(shape).toarray())
print("\n", H.matrix(shape).toarray())
print(H.matrix(shape).toarray())
vals, vecs = H.eigs(shape)
print(vals)
print(vecs)