def test_gauss4d_tri():
q = gauss4d_tri(3, 3)
result = quadrature(lambda x: 1, q)
np.testing.assert_almost_equal(result, 0.25)
result = quadrature(lambda x: (x[:, 0] * x[:, 1] * x[:, 2] * x[:, 3])**2,
q)
np.testing.assert_almost_equal(result, 1.0 / (180.0**2), 10)
def test_tanh_sinh():
q = map_to(tanh_sinh(3), [0, 1])
res = quadrature(lambda x: np.log(x), q)
np.testing.assert_almost_equal(res, -1.0)
q = map_to(tanh_sinh(3), [0, 1])
res = quadrature(lambda x: np.cos(x), q)
np.testing.assert_almost_equal(res, np.sin(1) - np.sin(0))
q = map_to(tanh_sinh(3), [0, 1])
res = quadrature(lambda x: x**2, q)
np.testing.assert_almost_equal(res, 1 / 3.0)
def test_cos_a2():
f = lambda x: np.cos(x)
exact = -1.48638536036015
for n in range(1, 13):
q = map_to(paget(n, 2), [0, 1])
res = quadrature(f, q)
np.testing.assert_almost_equal(res, exact)
def test_cos_a1():
f = lambda x: np.cos(x)
exact = -0.23981174200056474
for n in range(1, 13):
q = map_to(paget(n, 1), [0, 1])
res = quadrature(f, q)
np.testing.assert_almost_equal(res, exact)
def test_coincident_real():
def f(p):
r = np.sqrt((p[:, 0] - p[:, 2])**2 + (p[:, 1] - p[:, 3])**2)
return 1.0 / r
est = [quadrature(lambda p: f(p), coincident_quad(nq)) for nq in [9, 10]]
np.testing.assert_almost_equal(est[0], est[1])
def test_edge_adj_real():
def f(p):
y2 = -p[:, 3]
r = np.sqrt((p[:, 0] - p[:, 2])**2 + (p[:, 1] - y2)**2)
return 1.0 / r
est = [quadrature(lambda p: f(p), edge_adj_quad(nq)) for nq in [9, 10]]
np.testing.assert_almost_equal(est[0], est[1])
def check_simple(q, digits):
est = quadrature(lambda p: 1.0, q)
np.testing.assert_almost_equal(est, 0.25, digits)
est = quadrature(lambda p: p[:, 0] * p[:, 1] * p[:, 2] * p[:, 3], q)
correct = 1.0 / 576.0
np.testing.assert_almost_equal(est, correct, digits)
est = quadrature(lambda p: p[:, 0]**6 * p[:, 1] * p[:, 3], q)
correct = 1.0 / 3024.0
np.testing.assert_almost_equal(est, correct, digits)
est = quadrature(lambda p: p[:, 0] * p[:, 1] * p[:, 3]**6, q)
correct = 1.0 / 1344.0
np.testing.assert_almost_equal(est, correct, digits)
est = quadrature(lambda p: p[:, 0] * p[:, 2]**6 * p[:, 3], q)
correct = 1.0 / 3024.0
np.testing.assert_almost_equal(est, correct, digits)
def test_gauss2d_tri3():
q = gauss2d_tri(7)
result = quadrature(lambda x: np.sin(np.exp(x[:, 0] * x[:, 1] * 5)), q)
np.testing.assert_almost_equal(result, 0.426659055902, 4)
def test_gauss2d_tri2():
q = gauss2d_tri(5)
result = quadrature(lambda x: x[:, 0]**3 * x[:, 1]**4, q)
np.testing.assert_almost_equal(result, 1.0 / 2520.0, 12)
def test_gauss2d_tri1():
q = gauss2d_tri(2)
result = quadrature(lambda x: 1, q)
np.testing.assert_almost_equal(result, 0.5)
def test_gauss():
est = quadrature(lambda x: x**7, map_to(gaussxw(4), [0, 1]))
exact = 1.0 / 8.0
np.testing.assert_almost_equal(est, exact)