def test_wigner6j_ignore_invalid():
N = np.arange(1, 2)
K = np.arange(-2, 3)[:, np.newaxis]
with pytest.raises(ValueError):
# should raise an error
wigner6j(N * 2, K * 2, 0, 0, 0, 0, ignore_invalid=False)
# should compute
wigner6j(N * 2, K * 2, 0, 0, 0, 0, ignore_invalid=True)
def test_wigner6j_GH13():
"""
Test for https://github.com/fujiisoup/py3nj/issues/13
"""
N = np.arange(10)
J = np.arange(11)[:, np.newaxis]
# should not fail
wigner6j(0, N * 2, N * 2, J * 2, 2, 2)
def test_wigner6j_value():
# scalar test
for six_j, expected in SIX_J:
six_j = (np.array(six_j) * 2).astype(int)
actual = wigner6j(*six_j)
assert np.allclose(actual, expected)
# test vector
six_j = np.array([six for six, _ in SIX_J]).T * 2
expected = np.array([value for _, value in SIX_J]).T
actual = wigner6j(*six_j.astype(int))
assert np.allclose(actual, expected)
def get_prefactors(labels):
dim, ll, LL = [np.array(vals) for vals in zip(*labels)]
wigner_6j_degrees = 2 * np.array([ll, ll, LL])
wigner_6j_spins = np.array([dim, dim, dim]) - 1
wigner_6j_factors = py3nj.wigner6j(*wigner_6j_degrees.astype(int),
*wigner_6j_spins)
prefactors = (-1)**(dim - 1 + LL) * (
2 * ll + 1) * np.sqrt(2 * LL + 1) * wigner_6j_factors
return {label: prefactor for label, prefactor in zip(labels, prefactors)}
def test_wigner6j():
n = 10000
n2 = 10
l2 = rng.randint(0, 40, size=n)
l3 = rng.randint(0, 40, size=n)
l4 = rng.randint(0, 40, size=n)
l5 = rng.randint(0, 40, size=n)
l6 = rng.randint(0, 40, size=n)
l, expected_all = wigner.drc6j(l2, l3, l4, l5, l6)
for _ in range(n2):
lindex = rng.randint(0, 40, n)
two_l1 = l[lindex]
actual = wigner6j(two_l1, l2, l3, l4, l5, l6)
expected = expected_all[np.arange(len(lindex)), lindex]
assert np.allclose(actual, expected)
def wigner6j(jj1, jj2, jj3, jj4, jj5, jj6):
"""
Calculate the Wigner 6-j symbol,
.. math::
\\left\\{\\begin{array}{ccc} j_1 & j_2 & j_3 \\\\ j_4 & j_5 & j_6 \\end{array} \\right\\}
Parameters
----------
jj1 : integer
Twice the value of :math:`j_1`.
jj2 : integer
Twice the value of :math:`j_2`.
jj3 : integer
Twice the value of :math:`j_3`.
jj4 : integer
Twice the value of :math:`j_4`.
jj5 : integer
Twice the value of :math:`j_5`.
jj6 : integer
Twice the value of :math:`j_6`.
Returns
-------
float
The result.
Notes
-----
This currently wraps the `py3nj <https://github.com/fujiisoup/py3nj>`_
implementation. The back-end may change in the future.
Examples
--------
>>> n2.angmom.wigner6j(2 * 3, 2 * 6, 2 * 5, 2 * 4, 2 * 6, 2 * 9)
-0.020558557070186504
"""
result = py3nj.wigner6j(jj1, jj2, jj3, jj4, jj5, jj6)
return result