def test_gradient():
msh = circular_mesh(200, 1.0)
bf = basis_from_nodes([0.0, 1.0])
gradient = bf.get_gradient_basis()
e = msh.elements[57]
chain_rule = gradient.chain_rule(e.mapping.get_jacobian(0.0))
value = np.array(gradient.evaluate(0, 0.5))
np.testing.assert_almost_equal(chain_rule * value,
-31.83229765 * np.ones(2))
def test_basis_nodes():
bf = basis_from_nodes([-1.0, 0.0, 1.0])
# Check to make sure the nodes are right
x = [1.0, 1.0]
my_assert(bf.evaluate(0, -1.0), 1.0)
my_assert(bf.evaluate(0, 0.0), 0.0)
my_assert(bf.evaluate(0, 1.0), 0.0)
my_assert(bf.evaluate(1, 0.0), 1.0)
my_assert(bf.evaluate(2, 1.0), 1.0)
def test_basis_derivative():
bf = basis_from_nodes([-1.0, 0.0, 1.0])
x_hat = 0.3
yd_exact1 = x_hat - 0.5
yd_exact2 = -2 * x_hat
yd_exact3 = x_hat + 0.5
yd_est1 = bf.get_gradient_basis().evaluate(0, x_hat)
yd_est2 = bf.get_gradient_basis().evaluate(1, x_hat)
yd_est3 = bf.get_gradient_basis().evaluate(2, x_hat)
my_assert(yd_exact1, yd_est1)
my_assert(yd_exact2, yd_est2)
my_assert(yd_exact3, yd_est3)
def test_basis_2nd_order():
bf = basis_from_nodes([-1.0, 0.0, 1.0])
# Test for 2nd degree polynomials
x_hat = 0.3
y_exact1 = 0.5 * x_hat * (x_hat - 1)
y_exact2 = (1 - x_hat) * (1 + x_hat)
y_exact3 = 0.5 * x_hat * (1 + x_hat)
y_est1 = bf.evaluate(0, x_hat)
y_est2 = bf.evaluate(1, x_hat)
y_est3 = bf.evaluate(2, x_hat)
my_assert(y_exact1, y_est1)
my_assert(y_exact2, y_est2)
my_assert(y_exact3, y_est3)
def test_mass_matrix_functional():
bf = basis_funcs.basis_from_nodes([0.001, 0.999])
msh = simple_line_mesh(2)
q = quadrature.gauss(2)
apply_to_elements(msh, "basis", bf, non_gen = True)
apply_to_elements(msh, "continuous", False, non_gen = True)
init_dofs(msh)
fnc_coeffs = interpolate(lambda x,d: [[1,2][x[0] >= 0]] * 2, msh)
apply_coeffs(msh, fnc_coeffs, "function_yay")
basis_grabber = lambda e: e.function_yay
m = mass_matrix_for_rhs(assemble_mass_matrix(msh, q, basis_grabber))
M_exact = [0.5, 0.5, 1.0, 1.0]
np.testing.assert_almost_equal(M_exact, m[0:4])