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_step_lengths():
df_copy = df.copy()
step_lengths = traja.step_lengths(df_copy)
actual = step_lengths.to_numpy()[:5]
expected = np.array(
[np.nan, 1.829_180_85, 1.489_402_04, 2.130_723_72, 2.172_887_24])
npt.assert_allclose(actual, expected)
assert len(step_lengths == len(df_copy))