rd.variance_matrix()

RotationalDiffusion.models.variance_matrix(lag_times, diffusion_coeffs, principal_axes=array([[1., 0., 0.], [0., 1., 0.], [0., 0., 1.]]), precomputed_Q_model=None)

Variances of quaternion component products of an ideal Brownian rotor with diffusion tensor \(D\).

Utilizes Equations 2-4, 6.3, and 6.4 from Favro (1960) as described by Linke et al. (2017).

Parameters:

lag_times: (N,) ndarray

Discrete lag times at which to compute the variance matrix.

diffusion_coeffs: (3,) ndarray

Trace of a diffusion tensor in its diagonal form / principal axis frame.

Returns:

V: (N, 3, 3) ndarray

Analytical variances of the quaternion products \(q_i q_j\).