def test_rl_quad():
N = 5
values = [(0.2, 0.3, 0.2949533988361775),
(1.2, 4.0, 0.04976184140700821),
(1.5, 1.5, 0.1216505480495554)]
for (ay, by, exact) in values:
qi = rl_quad(N + 1, ay, by)
qx = np.array(qi.x)
qw = np.array(qi.w)
gll_nodes = gll_basis(N).nodes
np.testing.assert_almost_equal(gll_nodes, qx)
f = lambda x: x ** 4 / np.sqrt((x - ay) ** 2 + by ** 2)
est = np.sum(f(qx) * qw)
# DUDE 13 digits!
np.testing.assert_almost_equal(est, exact, 13)
def test_gll_basis():
bf = gll_basis(9)
x_val = 0.9195339081664588138289 * 0.5 + 0.5
x = [x_val, x_val]
val = bf.evaluate(8, x_val)
np.testing.assert_almost_equal(val, [1.0, 1.0])