def test_interrelations_k_exact(self):
n = 7
x = 5.746161870059113
left = np.complex(sph_kn_exact(n, x))
right = np.complex((-1)**(n + 1) * pi / 2 *
(sph_i1n_exact(n, x) - sph_i2n_exact(n, x)))
assert_allclose(left, right)
def test_sph_i12_exact(self):
x = 9.810801919951345
desired = (1 / x + 3 / x ** 3) * np.sinh(x) - 3 / x ** 2 * np.cosh(x)
actual = np.complex(sph_i1n_exact(2, x))
assert_allclose(actual, desired)
def test_sph_i11_exact(self):
x = 6.802805007381322
desired = -np.sinh(x) / x ** 2 + np.cosh(x) / x
actual = np.complex(sph_i1n_exact(1, x))
assert_allclose(actual, desired)
def test_sph_i10_exact(self):
x = 62.3
desired = np.sinh(x) / x
actual = np.complex(sph_i1n_exact(0, x))
assert_allclose(actual, desired)
def test_interrelations_i1_exact(self):
n = 3
x = 1.9513017144556937
left = np.complex(sph_i1n_exact(n, x))
right = np.complex(mpc(0, 1) ** (-n) * sph_jn_exact(n, 1j * x))
assert_allclose(left, right)
def test_interrelations_k_exact(self):
n = 7
x = 5.746161870059113
left = np.complex(sph_kn_exact(n, x))
right = np.complex((-1) ** (n + 1) * pi / 2 * (sph_i1n_exact(n, x) - sph_i2n_exact(n, x)))
assert_allclose(left, right)
def test_sph_i12_exact(self):
x = 9.810801919951345
desired = (1 / x + 3 / x**3) * np.sinh(x) - 3 / x**2 * np.cosh(x)
actual = np.complex(sph_i1n_exact(2, x))
assert_allclose(actual, desired)
def test_sph_i11_exact(self):
x = 6.802805007381322
desired = -np.sinh(x) / x**2 + np.cosh(x) / x
actual = np.complex(sph_i1n_exact(1, x))
assert_allclose(actual, desired)
def test_sph_i10_exact(self):
x = 62.3
desired = np.sinh(x) / x
actual = np.complex(sph_i1n_exact(0, x))
assert_allclose(actual, desired)
def test_interrelations_i1_exact(self):
n = 3
x = 1.9513017144556937
left = np.complex(sph_i1n_exact(n, x))
right = np.complex(mpc(0, 1)**(-n) * sph_jn_exact(n, 1j * x))
assert_allclose(left, right)
