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)
def test_matrix_1d_coeffs_nonuni(self):
shape = 11,
x = np.linspace(0, 10, 11)
L = Coef(x) * FinDiff(0, x, 2)
u = np.random.rand(*shape).reshape(-1)
actual = L.matrix(shape).dot(u)
expected = L(u).reshape(-1)
np.testing.assert_array_almost_equal(expected, actual)
def test_2d_inhom_var_coefs_with_identity_all_dirichlet(self):
shape = (5, 5)
(x, y), (dx, dy), (X, Y) = make_grid(shape, edges=[(-1, 1), (-1, 1)])
expected = X**3 + Y**3 + X * Y + 1
#L = Coef(3*X) * FinDiff(0, dx, 2) + Coef(2*Y) * FinDiff((0, dx, 1), (1, dy, 1)) + FinDiff(1, dy, 2) + Coef(5*X*Y) * Identity()
L = Coef(5 * X * Y) * FinDiff(0, dx, 2) #Identity()
#f = 18 * X**2 + 8*Y + 5*X*Y*expected
mat = L.matrix(shape)
print(mat)
bc = BoundaryConditions(shape)
bc[0, :] = expected
bc[-1, :] = expected
bc[:, 0] = expected
bc[:, -1] = expected
pde = PDE(L, f, bc)
actual = pde.solve()
np.testing.assert_array_almost_equal(expected, actual, decimal=4)