Merge pull request #131 from jorenham/fix-theta_m_bar

Fix `constants.theta_m_bar`

lmo/constants.py

@@ -9,18 +9,18 @@
 
 theta_m: Final[float] = 0.955316618124509278163857102515757754
 r"""
-Magic angle \( \theta_m = \arctan \sqrt 2 \approx 0.9553 \).
+Magic angle \( \theta_m = \arctan \sqrt 2 \).
 
 See also:
-    - https://wikipedia.org/wiki/Magic_angle
+    - [Magic angle - Wikipedia](https://wikipedia.org/wiki/Magic_angle)
 """
 
-theta_m_bar: Final[float] = 0.221389709640985827437970269154380360
+theta_m_bar: Final[float] = 0.152043361992348182457286110194392272
 r"""
-Magic number of turns \( \bar{\theta}_m = \theta_m / (2 \pi) \approx 0.2214 \)
+Magic number of turns \( \bar{\theta}_m = \theta_m / (2 \pi) \).
 
 See also:
-    - [theta_m][lmo.constants.theta_m]
-    - https://wikipedia.org/wiki/Magic_angle
-    - https://wikipedia.org/wiki/Turn_(angle)
+    - [`lmo.constants.theta_m`][lmo.constants.theta_m]
+    - [Magic angle - Wikipedia](https://wikipedia.org/wiki/Magic_angle)
+    - [Turn (angle) - Wikipedia](https://wikipedia.org/wiki/Turn_(angle))
 """

tests/test_theoretical.py

@@ -111,7 +111,7 @@ def test_lm_normal():
     r = [1, 2, 3, 4]
 
     l2 = sigma / np.sqrt(np.pi)
-    l = np.array([mu, l2, 0, l2 * (30 * constants.theta_m / np.pi - 9)])
+    l = np.array([mu, l2, 0, l2 * (60 * constants.theta_m_bar - 9)])
 
     l_ppf = l_moment_from_ppf(IQ.inv_cdf, r)
     assert_allclose(l_ppf, l)
@@ -132,7 +132,7 @@ def test_tlm_normal():
 
     r = [1, 2, 3, 4]
 
-    tl2 = 6 * sigma / np.sqrt(np.pi) * (1 - 3 * constants.theta_m / np.pi)
+    tl2 = 6 * sigma / np.sqrt(np.pi) * (1 - 6 * constants.theta_m_bar)
     tl = np.array([mu, tl2, 0, tl2 * 0.06247999167])
 
     tl_ppf = l_moment_from_ppf(IQ.inv_cdf, r, trim=1)