def _tof_equation_y(x, y, T0, ll, M):
"""Time of flight equation with externally computated y."""
if M == 0 and np.sqrt(0.6) < x < np.sqrt(1.4):
eta = y - ll * x
S_1 = (1 - ll - x * eta) * 0.5
Q = 4 / 3 * hyp2f1b(S_1)
T_ = (eta**3 * Q + 4 * ll * eta) * 0.5
else:
psi = _compute_psi(x, y, ll)
T_ = np.divide(
np.divide(psi + M * pi, np.sqrt(np.abs(1 - x**2))) - x + ll * y,
(1 - x**2),
)
return T_ - T0
def _tof_equation(x, y, T0, ll, M):
"""Time of flight equation.
"""
if M == 0 and np.sqrt(0.6) < x < np.sqrt(1.4):
eta = y - ll * x
S_1 = (1 - ll - x * eta) * .5
Q = 4 / 3 * hyp2f1b(S_1)
T_ = (eta ** 3 * Q + 4 * ll * eta) * .5
else:
psi = _compute_psi(x, y, ll)
T_ = np.divide(np.divide(psi + M * pi,
np.sqrt(np.abs(1 - x ** 2))) - x + ll * y,
(1 - x ** 2))
return T_ - T0