Rotations in cryo-EM

cryojax.rotations implements an engine and utility functions for rotations in cryo-EM.

Representing rotations

The engine for handling rotations in cryoJAX is the cryojax.rotations.SO3 class. This is based on the implementation in the package jaxlie.

cryojax.rotations.SO3

A rotation in 3D space, represented by the SO3 matrix lie group.

The class is almost exactly derived from the jaxlie.SO3 object.

jaxlie was written for Yi, Brent, et al. 2021.

__init__

__init__(wxyz: Float[NDArrayLike, '4'])

Arguments:

• wxyz: A quaternion represented as \((q_w, q_x, q_y, q_z)\).

apply

apply(target: Float[Array, '3']) -> Float[Array, '3']

compose

compose(other: typing.Self) -> typing.Self

inverse

inverse() -> typing.Self

from_x_radians classmethod

from_x_radians(angle: Float[Array, '']) -> typing.Self

Generates a x-axis rotation.

from_y_radians classmethod

from_y_radians(angle: Float[Array, '']) -> typing.Self

Generates a x-axis rotation.

from_z_radians classmethod

from_z_radians(angle: Float[Array, '']) -> typing.Self

Generates a x-axis rotation.

identity classmethod

identity() -> typing.Self

from_matrix classmethod

from_matrix(matrix: Float[Array, '3 3']) -> typing.Self

as_matrix

as_matrix() -> Float[Array, '3 3']

exp classmethod

exp(tangent: Float[Array, '3']) -> typing.Self

log

log() -> Float[Array, '3']

adjoint

adjoint() -> Float[Array, '3 3']

Computes the adjoint, which transforms tangent vectors between tangent spaces.

normalize

normalize() -> typing.Self

sample_uniform classmethod

sample_uniform(key: PRNGKeyArray) -> typing.Self

Utilities for converting between angular parametrizations