def I1(h2, k2, s):
res = (ellip_harm_2(h2, k2, 1, 1, s) /
(3 * ellip_harm(h2, k2, 1, 1, s)) +
ellip_harm_2(h2, k2, 1, 2, s) /
(3 * ellip_harm(h2, k2, 1, 2, s)) +
ellip_harm_2(h2, k2, 1, 3, s) /
(3 * ellip_harm(h2, k2, 1, 3, s)))
return res
def test_ellip_harm_invalid_p():
# Regression test. This should return nan.
n = 4
# Make p > 2*n + 1.
p = 2 * n + 2
result = ellip_harm(0.5, 2.0, n, p, 0.2)
assert np.isnan(result)
def solid_int_ellip2(lambda1, mu, nu, n, p, h2, k2):
return (ellip_harm_2(h2, k2, n, p, lambda1)
* ellip_harm(h2, k2, n, p, mu)*ellip_harm(h2, k2, n, p, nu))
def test_ellip_harm():
def E01(h2, k2, s):
return 1
def E11(h2, k2, s):
return s
def E12(h2, k2, s):
return sqrt(abs(s*s - h2))
def E13(h2, k2, s):
return sqrt(abs(s*s - k2))
def E21(h2, k2, s):
return s*s - 1/3*((h2 + k2) + sqrt(abs((h2 + k2)*(h2 + k2)-3*h2*k2)))
def E22(h2, k2, s):
return s*s - 1/3*((h2 + k2) - sqrt(abs((h2 + k2)*(h2 + k2)-3*h2*k2)))
def E23(h2, k2, s):
return s * sqrt(abs(s*s - h2))
def E24(h2, k2, s):
return s * sqrt(abs(s*s - k2))
def E25(h2, k2, s):
return sqrt(abs((s*s - h2)*(s*s - k2)))
def E31(h2, k2, s):
return s*s*s - (s/5)*(2*(h2 + k2) + sqrt(4*(h2 + k2)*(h2 + k2) -
15*h2*k2))
def E32(h2, k2, s):
return s*s*s - (s/5)*(2*(h2 + k2) - sqrt(4*(h2 + k2)*(h2 + k2) -
15*h2*k2))
def E33(h2, k2, s):
return sqrt(abs(s*s - h2))*(s*s - 1/5*((h2 + 2*k2) + sqrt(abs((h2 +
2*k2)*(h2 + 2*k2) - 5*h2*k2))))
def E34(h2, k2, s):
return sqrt(abs(s*s - h2))*(s*s - 1/5*((h2 + 2*k2) - sqrt(abs((h2 +
2*k2)*(h2 + 2*k2) - 5*h2*k2))))
def E35(h2, k2, s):
return sqrt(abs(s*s - k2))*(s*s - 1/5*((2*h2 + k2) + sqrt(abs((2*h2
+ k2)*(2*h2 + k2) - 5*h2*k2))))
def E36(h2, k2, s):
return sqrt(abs(s*s - k2))*(s*s - 1/5*((2*h2 + k2) - sqrt(abs((2*h2
+ k2)*(2*h2 + k2) - 5*h2*k2))))
def E37(h2, k2, s):
return s * sqrt(abs((s*s - h2)*(s*s - k2)))
assert_equal(ellip_harm(5, 8, 1, 2, 2.5, 1, 1),
ellip_harm(5, 8, 1, 2, 2.5))
known_funcs = {(0, 1): E01, (1, 1): E11, (1, 2): E12, (1, 3): E13,
(2, 1): E21, (2, 2): E22, (2, 3): E23, (2, 4): E24,
(2, 5): E25, (3, 1): E31, (3, 2): E32, (3, 3): E33,
(3, 4): E34, (3, 5): E35, (3, 6): E36, (3, 7): E37}
point_ref = []
def ellip_harm_known(h2, k2, n, p, s):
for i in range(h2.size):
func = known_funcs[(int(n[i]), int(p[i]))]
point_ref.append(func(h2[i], k2[i], s[i]))
return point_ref
np.random.seed(1234)
h2 = np.random.pareto(0.5, size=30)
k2 = h2*(1 + np.random.pareto(0.5, size=h2.size))
s = np.random.pareto(0.5, size=h2.size)
points = []
for i in range(h2.size):
for n in range(4):
for p in range(1, 2*n+2):
points.append((h2[i], k2[i], n, p, s[i]))
points = np.array(points)
assert_func_equal(ellip_harm, ellip_harm_known, points, rtol=1e-12)
def I1(h2, k2, s):
res = (ellip_harm_2(h2, k2, 1, 1, s)/(3 * ellip_harm(h2, k2, 1, 1, s))
+ ellip_harm_2(h2, k2, 1, 2, s)/(3 * ellip_harm(h2, k2, 1, 2, s)) +
ellip_harm_2(h2, k2, 1, 3, s)/(3 * ellip_harm(h2, k2, 1, 3, s)))
return res
def solid_int_ellip2(lambda1, mu, nu, n, p, h2, k2):
return (ellip_harm_2(h2, k2, n, p, lambda1) *
ellip_harm(h2, k2, n, p, mu) * ellip_harm(h2, k2, n, p, nu))
def test_ellip_harm():
def E01(h2, k2, s):
return 1
def E11(h2, k2, s):
return s
def E12(h2, k2, s):
return sqrt(abs(s * s - h2))
def E13(h2, k2, s):
return sqrt(abs(s * s - k2))
def E21(h2, k2, s):
return s * s - 1 / 3 * (
(h2 + k2) + sqrt(abs((h2 + k2) * (h2 + k2) - 3 * h2 * k2)))
def E22(h2, k2, s):
return s * s - 1 / 3 * (
(h2 + k2) - sqrt(abs((h2 + k2) * (h2 + k2) - 3 * h2 * k2)))
def E23(h2, k2, s):
return s * sqrt(abs(s * s - h2))
def E24(h2, k2, s):
return s * sqrt(abs(s * s - k2))
def E25(h2, k2, s):
return sqrt(abs((s * s - h2) * (s * s - k2)))
def E31(h2, k2, s):
return s * s * s - (s / 5) * (2 * (h2 + k2) +
sqrt(4 * (h2 + k2) *
(h2 + k2) - 15 * h2 * k2))
def E32(h2, k2, s):
return s * s * s - (s / 5) * (2 * (h2 + k2) -
sqrt(4 * (h2 + k2) *
(h2 + k2) - 15 * h2 * k2))
def E33(h2, k2, s):
return sqrt(abs(s * s - h2)) * (s * s - 1 / 5 * (
(h2 + 2 * k2) +
sqrt(abs((h2 + 2 * k2) * (h2 + 2 * k2) - 5 * h2 * k2))))
def E34(h2, k2, s):
return sqrt(abs(s * s - h2)) * (s * s - 1 / 5 * (
(h2 + 2 * k2) -
sqrt(abs((h2 + 2 * k2) * (h2 + 2 * k2) - 5 * h2 * k2))))
def E35(h2, k2, s):
return sqrt(abs(s * s - k2)) * (s * s - 1 / 5 * (
(2 * h2 + k2) +
sqrt(abs((2 * h2 + k2) * (2 * h2 + k2) - 5 * h2 * k2))))
def E36(h2, k2, s):
return sqrt(abs(s * s - k2)) * (s * s - 1 / 5 * (
(2 * h2 + k2) -
sqrt(abs((2 * h2 + k2) * (2 * h2 + k2) - 5 * h2 * k2))))
def E37(h2, k2, s):
return s * sqrt(abs((s * s - h2) * (s * s - k2)))
assert_equal(ellip_harm(5, 8, 1, 2, 2.5, 1, 1),
ellip_harm(5, 8, 1, 2, 2.5))
known_funcs = {
(0, 1): E01,
(1, 1): E11,
(1, 2): E12,
(1, 3): E13,
(2, 1): E21,
(2, 2): E22,
(2, 3): E23,
(2, 4): E24,
(2, 5): E25,
(3, 1): E31,
(3, 2): E32,
(3, 3): E33,
(3, 4): E34,
(3, 5): E35,
(3, 6): E36,
(3, 7): E37
}
point_ref = []
def ellip_harm_known(h2, k2, n, p, s):
for i in range(h2.size):
func = known_funcs[(int(n[i]), int(p[i]))]
point_ref.append(func(h2[i], k2[i], s[i]))
return point_ref
np.random.seed(1234)
h2 = np.random.pareto(0.5, size=30)
k2 = h2 * (1 + np.random.pareto(0.5, size=h2.size))
s = np.random.pareto(0.5, size=h2.size)
points = []
for i in range(h2.size):
for n in range(4):
for p in range(1, 2 * n + 2):
points.append((h2[i], k2[i], n, p, s[i]))
points = np.array(points)
assert_func_equal(ellip_harm, ellip_harm_known, points, rtol=1e-12)