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Representing poses¤

cryojax provides different parameterizations for the pose of a structure. These are captured through the abstract base class called AbstractPose.

cryojax.simulator.AbstractPose

cryojax.simulator.AbstractPose ¤

Base class for the image pose. Subclasses will choose a particular convention for parameterizing the rotation by overwriting the AbstractPose.rotation property.

cryojax.simulator.AbstractPose.compute_shifts(frequency_grid_in_angstroms: Float[Array, 'y_dim x_dim 2']) -> Complex[Array, 'y_dim x_dim'] ¤

Compute the phase shifts from the in-plane translation, given a frequency grid coordinate system.

Arguments:

  • frequency_grid_in_angstroms: A grid of in-plane frequency coordinates \((q_x, q_y)\)

Returns:

From the vector \((t_x, t_y)\) (given by self.offset_in_angstroms), returns the grid of in-plane phase shifts \(\exp{(- 2 \pi i (t_x q_x + t_y q_y))}\).

cryojax.simulator.AbstractPose.rotate_coordinates(coordinate_grid_or_list: Float[Array, 'z_dim y_dim x_dim 3'] | Float[Array, 'size 3'], inverse: bool = False) -> Float[Array, 'z_dim y_dim x_dim 3'] | Float[Array, 'size 3'] ¤
rotate_coordinates(coordinate_grid_or_list: Float[Array, 'z_dim y_dim x_dim 3'], inverse: bool = False) -> Float[Array, 'z_dim y_dim x_dim 3']

rotate_coordinates(coordinate_grid_or_list: Float[Array, 'size 3'], inverse: bool = False) -> Float[Array, 'size 3']

Rotate a 3D coordinate system.

Arguments:

  • coordinate_grid_or_list: The 3D coordinate system to rotate. This can either be a list of coordinates of shape (N, 3) or a grid of coordinates (N1, N2, N3, 3).
  • inverse: If True, compute the inverse rotation (i.e. rotation by the matrix \(R^T\), where \(R\) is the rotation matrix).

Returns:

The rotated version of coordinate_grid_or_list.

cryojax.simulator.AbstractPose.offset_in_angstroms: Float[Array, 2] cached property ¤

The in-plane translation vector, where the origin in taken to be in the center of the imaging plane.

cryojax.simulator.AbstractPose.rotation: SO3 abstractmethod cached property ¤

Generate an SO3 object from a particular angular parameterization.

cryojax.simulator.AbstractPose.from_rotation(rotation: SO3) -> Self abstractmethod classmethod ¤

Construct an AbstractPose from an SO3 object.

cryojax.simulator.AbstractPose.from_rotation_and_translation(rotation: SO3, offset_in_angstroms: Float[Array, 2]) -> Self classmethod ¤

Construct an AbstractPose from an SO3 object and an in-plane translation vector.

cryojax.simulator.EulerAnglePose ¤

An AbstractPose represented by Euler angles. Angles are given in degrees, and the sequence of rotations is given by a zyz extrinsic rotations.

cryojax.simulator.EulerAnglePose.__init__(offset_x_in_angstroms: float | Float[Array, ''] = 0.0, offset_y_in_angstroms: float | Float[Array, ''] = 0.0, view_phi: float | Float[Array, ''] = 0.0, view_theta: float | Float[Array, ''] = 0.0, view_psi: float | Float[Array, ''] = 0.0) ¤

Arguments:

  • offset_x_in_angstroms: In-plane translation in x direction.
  • offset_y_in_angstroms: In-plane translation in y direction.
  • view_phi: Angle to rotate about first rotation axis, which is the z axis.
  • view_theta: Angle to rotate about second rotation axis, which is the y axis.
  • view_psi: Angle to rotate about third rotation axis, which is the z axis.

cryojax.simulator.QuaternionPose ¤

An AbstractPose represented by unit quaternions.

cryojax.simulator.QuaternionPose.__init__(offset_x_in_angstroms: float | Float[Array, ''] = 0.0, offset_y_in_angstroms: float | Float[Array, ''] = 0.0, wxyz: tuple[float, float, float, float] | Float[np.ndarray, 4] | Float[Array, 4] = (1.0, 0.0, 0.0, 0.0)) ¤

Arguments:

  • offset_x_in_angstroms: In-plane translation in x direction.
  • offset_y_in_angstroms: In-plane translation in y direction.
  • wxyz: The quaternion, represented as a vector \(\mathbf{q} = (q_w, q_x, q_y, q_z)\).

cryojax.simulator.AxisAnglePose ¤

An AbstractPose parameterized in the axis-angle representation.

The axis-angle representation parameterizes elements of the so3 algebra, which are skew-symmetric matrices, with the euler vector \(\boldsymbol{\omega} = (\omega_x, \omega_y, \omega_z)\). The magnitude of this vector is the angle, and the unit vector is the axis.

In a SO3 object, the euler vector is mapped to SO3 group elements using the matrix exponential.

cryojax.simulator.AxisAnglePose.__init__(offset_x_in_angstroms: float | Float[Array, ''] = 0.0, offset_y_in_angstroms: float | Float[Array, ''] = 0.0, euler_vector: tuple[float, float, float] | Float[np.ndarray, 3] | Float[Array, 3] = (0.0, 0.0, 0.0)) ¤

Arguments:

  • offset_x_in_angstroms: In-plane translation in x direction.
  • offset_y_in_angstroms: In-plane translation in y direction.
  • euler_vector: The axis-angle parameterization, represented with the euler vector \(\boldsymbol{\omega}\).