def expected_sq_displacement(trj: TrajaDataFrame,
n: int = 0,
eqn1: bool = True) -> float:
"""Expected displacement.
.. note::
This method is experimental and needs testing.
"""
sl = traja.step_lengths(trj)
ta = traja.angles(trj)
l = np.mean(sl)
l2 = np.mean(sl**2)
c = np.mean(np.cos(ta))
s = np.mean(np.sin(ta))
s2 = s**2
if eqn1:
# Eqn 1
alpha = np.arctan2(s, c)
gamma = ((1 - c)**2 - s2) * np.cos(
(n + 1) * alpha) - 2 * s * (1 - c) * np.sin((n + 1) * alpha)
esd = (n * l2 + 2 * l**2 * ((c - c**2 - s2) * n - c) /
((1 - c)**2 + s2) + 2 * l**2 * ((2 * s2 +
(c + s2)**((n + 1) / 2)) /
((1 - c)**2 + s2)**2) * gamma)
return abs(esd)
else:
logger.info("This method is experimental and requires testing.")
# Eqn 2
esd = n * l2 + 2 * l**2 * c / (1 - c) * (n - (1 - c**n) / (1 - c))
return esd
def test_angles(lag):
df_copy = df.copy()
angles = traja.angles(df_copy, lag=lag)
actual = angles.to_numpy()
if lag == 1:
expected = np.array([
np.nan,
50.536_377_13,
62.000_036_72,
89.961_185_41,
25.764_324_08,
27.737_271_33,
0.259_677_63,
26.958_350_61,
22.622_286,
19.665_283_71,
31.428_064_33,
35.554_608_67,
77.216_475_78,
80.981_399_37,
77.495_666_91,
64.779_921_95,
55.220_856_61,
12.418_644_03,
18.295_995_36,
9.327_266_35,
])
elif lag == 2:
expected = np.array([
np.nan,
np.nan,
55.679_398_79,
78.552_154_19,
57.510_652_27,
1.318_153_96,
11.741_160_75,
10.869_226_84,
24.615_298_57,
21.161_131_62,
26.022_239_16,
33.485_645_28,
55.060_685_9,
88.237_494_22,
79.351_771_4,
71.545_102_77,
59.557_726_58,
33.248_128_63,
15.505_016_09,
13.817_221_74,
])
npt.assert_allclose(actual, expected)