def test_rl_quad_more_difficult():
N = 7
values = [(0.2, 0.3, 0.7565395005),
(1.2, 4.0, 0.003080702117),
(1.5, 1.5, 0.04518013019)]
for (ay, by, exact) in values:
qi = rl_quad(N, ay, by)
qx = np.array(qi.x)
qw = np.array(qi.w)
f = lambda x: x ** 4 / (np.sqrt((x - ay) ** 2 + by ** 2) ** 3)
est = np.sum(f(qx) * qw)
# DUDE 13 digits!
np.testing.assert_almost_equal(est, exact, 3)
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)