pySymStat 1.0

pySymStat is a Python program package designed for solving statistic problem (mean and variance) of spatial rotations and projection directions when molecular symmetries are considered.

This program package implements algorithm proposed in the paper "The Moments of Orientation Estimations Considering Molecular Symmetry in Cryo-EM", written by Qi ZHANG, Chenlong BAO, Hai LIN, Mingxu HU. Users may consult our paper for more details.

We provide a demo program demo/demo.py which shows how to use our package for solving these two problems. As an example, we present how to solve mean and variance of spatial rotations.

    mean, variance, representatives, solutions = meanvar_SO3_G(quats, sym_grp, type = 'arithmetic')

Here quats is a $n$ by $4$ numpy array, and quats[i, :] is the unit quaternion representation of $i$-th spatial rotation. sym_grp is a string representing a molecular symmetry group. Note that there are only five possible class of molecular symmetry groups, i.e., CN, DN, T, O and I, where N is a positive integer. There are some other options, e.g., the type of distance can be arithmetic or geometric. Then this function returns not only mean and variance but also other informations like representatives and optimal group elements. One may consult our paper for their meaning in details.

Similarly, one can call the function projection_direction_mean_variance_S2_G for solving mean and variance of projection directions with molecular symmetries.

    mean, variance, representatives, solutions = meanvar_S2_G(vecs, sym_grp, type = 'arithmetic')

Here vecs is a $n$ by $3$ numpy array, and $i$-th projection direction $vecs[i, :]$ is a unit 3-vector.