Module matrix_ops

Module for the handling of Frame Order.

Classes

Data
A data container stored in the memo objects for use by the Result_command class.

Functions

daeg_to_rotational_superoperator(daeg, Rsuper)
Convert the frame order matrix (daeg) to the rotational superoperator.

float pcs_pivot_motion_full(theta_i, phi_i, sigma_i, r_pivot_atom, r_ln_pivot, A, R_eigen, RT_eigen, Ri_prime)
Calculate the PCS value after a pivoted motion for the isotropic cone model.

pcs_pivot_motion_full_qrint(theta_i=None, phi_i=None, sigma_i=None, full_in_ref_frame=None, r_pivot_atom=None, r_pivot_atom_rev=None, r_ln_pivot=None, A=None, R_eigen=None, RT_eigen=None, Ri_prime=None, pcs_theta=None, pcs_theta_err=None, missing_pcs=None, error_flag=False)
Calculate the PCS value after a pivoted motion for the isotropic cone model.

float pcs_pivot_motion_torsionless(theta_i, phi_i, r_pivot_atom, r_ln_pivot, A, R_eigen, RT_eigen, Ri_prime)
Calculate the PCS value after a pivoted motion for the isotropic cone model.

pcs_pivot_motion_torsionless_qrint(theta_i=None, phi_i=None, full_in_ref_frame=None, r_pivot_atom=None, r_pivot_atom_rev=None, r_ln_pivot=None, A=None, R_eigen=None, RT_eigen=None, Ri_prime=None, pcs_theta=None, pcs_theta_err=None, missing_pcs=None, error_flag=False)
Calculate the PCS value after a pivoted motion for the isotropic cone model.

reduce_alignment_tensor(D, A, red_tensor)
Calculate the reduction in the alignment tensor caused by the Frame Order matrix.

reduce_alignment_tensor_symmetric(D, A, red_tensor)
Calculate the reduction in the alignment tensor caused by the Frame Order matrix.

rotate_daeg(matrix, Rx2_eigen)
Rotate the given frame order matrix.

Variables

__package__ = 'lib.frame_order'

Imports: cos, sin, dot, inner, sqrt, transpose, norm, transpose_23, tilt_torsion_to_R

Function Details

daeg_to_rotational_superoperator(daeg, Rsuper)

Convert the frame order matrix (daeg) to the rotational superoperator.

Parameters:

• daeg (numpy 9D, rank-2 array or numpy 3D, rank-4 array) - The second degree frame order matrix, daeg. This must be in the Kronecker product layout.
• Rsuper (numpy 5D, rank-2 array) - The rotational superoperator structure to be populated.

pcs_pivot_motion_full(theta_i, phi_i, sigma_i, r_pivot_atom, r_ln_pivot, A, R_eigen, RT_eigen, Ri_prime)

Calculate the PCS value after a pivoted motion for the isotropic cone model.

Parameters:

• theta_i (float) - The half cone opening angle (polar angle).
• phi_i (float) - The cone azimuthal angle.
• sigma_i (float) - The torsion angle for state i.
• r_pivot_atom (numpy rank-1, 3D array) - The pivot point to atom vector.
• r_ln_pivot (numpy rank-1, 3D array) - The lanthanide position to pivot point vector.
• A (numpy rank-2, 3D array) - The full alignment tensor of the non-moving domain.
• R_eigen (numpy rank-2, 3D array) - The eigenframe rotation matrix.
• RT_eigen (numpy rank-2, 3D array) - The transpose of the eigenframe rotation matrix (for faster calculations).
• Ri_prime (numpy rank-2, 3D array) - The empty rotation matrix for the in-frame isotropic cone motion for state i.

Returns: float

The PCS value for the changed position.

pcs_pivot_motion_full_qrint(theta_i=None, phi_i=None, sigma_i=None, full_in_ref_frame=None, r_pivot_atom=None, r_pivot_atom_rev=None, r_ln_pivot=None, A=None, R_eigen=None, RT_eigen=None, Ri_prime=None, pcs_theta=None, pcs_theta_err=None, missing_pcs=None, error_flag=False)

Calculate the PCS value after a pivoted motion for the isotropic cone model.

Parameters:

• theta_i (float) - The half cone opening angle (polar angle).
• phi_i (float) - The cone azimuthal angle.
• sigma_i (float) - The torsion angle for state i.
• full_in_ref_frame (numpy rank-1 array) - An array of flags specifying if the tensor in the reference frame is the full or reduced tensor.
• r_pivot_atom (numpy rank-2, 3D array) - The pivot point to atom vector.
• r_pivot_atom_rev (numpy rank-2, 3D array) - The reversed pivot point to atom vector.
• r_ln_pivot (numpy rank-2, 3D array) - The lanthanide position to pivot point vector.
• A (numpy rank-2, 3D array) - The full alignment tensor of the non-moving domain.
• R_eigen (numpy rank-2, 3D array) - The eigenframe rotation matrix.
• RT_eigen (numpy rank-2, 3D array) - The transpose of the eigenframe rotation matrix (for faster calculations).
• Ri_prime (numpy rank-2, 3D array) - The empty rotation matrix for the in-frame isotropic cone motion for state i.
• pcs_theta (numpy rank-2 array) - The storage structure for the back-calculated PCS values.
• pcs_theta_err (numpy rank-2 array) - The storage structure for the back-calculated PCS errors.
• missing_pcs (numpy rank-2 array) - A structure used to indicate which PCS values are missing.
• error_flag (bool) - A flag which if True will cause the PCS errors to be estimated and stored in pcs_theta_err.

pcs_pivot_motion_torsionless(theta_i, phi_i, r_pivot_atom, r_ln_pivot, A, R_eigen, RT_eigen, Ri_prime)

Calculate the PCS value after a pivoted motion for the isotropic cone model.

Parameters:

• theta_i (float) - The half cone opening angle (polar angle).
• phi_i (float) - The cone azimuthal angle.
• r_pivot_atom (numpy rank-1, 3D array) - The pivot point to atom vector.
• r_ln_pivot (numpy rank-1, 3D array) - The lanthanide position to pivot point vector.
• A (numpy rank-2, 3D array) - The full alignment tensor of the non-moving domain.
• R_eigen (numpy rank-2, 3D array) - The eigenframe rotation matrix.
• RT_eigen (numpy rank-2, 3D array) - The transpose of the eigenframe rotation matrix (for faster calculations).
• Ri_prime (numpy rank-2, 3D array) - The empty rotation matrix for the in-frame isotropic cone motion for state i.

Returns: float

The PCS value for the changed position.

pcs_pivot_motion_torsionless_qrint(theta_i=None, phi_i=None, full_in_ref_frame=None, r_pivot_atom=None, r_pivot_atom_rev=None, r_ln_pivot=None, A=None, R_eigen=None, RT_eigen=None, Ri_prime=None, pcs_theta=None, pcs_theta_err=None, missing_pcs=None, error_flag=False)

Calculate the PCS value after a pivoted motion for the isotropic cone model.

Parameters:

• theta_i (float) - The half cone opening angle (polar angle).
• phi_i (float) - The cone azimuthal angle.
• full_in_ref_frame (numpy rank-1 array) - An array of flags specifying if the tensor in the reference frame is the full or reduced tensor.
• r_pivot_atom (numpy rank-2, 3D array) - The pivot point to atom vector.
• r_pivot_atom_rev (numpy rank-2, 3D array) - The reversed pivot point to atom vector.
• r_ln_pivot (numpy rank-2, 3D array) - The lanthanide position to pivot point vector.
• A (numpy rank-2, 3D array) - The full alignment tensor of the non-moving domain.
• R_eigen (numpy rank-2, 3D array) - The eigenframe rotation matrix.
• RT_eigen (numpy rank-2, 3D array) - The transpose of the eigenframe rotation matrix (for faster calculations).
• Ri_prime (numpy rank-2, 3D array) - The empty rotation matrix for the in-frame isotropic cone motion for state i.
• pcs_theta (numpy rank-2 array) - The storage structure for the back-calculated PCS values.
• pcs_theta_err (numpy rank-2 array) - The storage structure for the back-calculated PCS errors.
• missing_pcs (numpy rank-2 array) - A structure used to indicate which PCS values are missing.
• error_flag (bool) - A flag which if True will cause the PCS errors to be estimated and stored in pcs_theta_err.

reduce_alignment_tensor(D, A, red_tensor)

Calculate the reduction in the alignment tensor caused by the Frame Order matrix.

This is both the forward rotation notation and Kronecker product arrangement.

Parameters:

• D (numpy 9D, rank-2 array) - The Frame Order matrix, 2nd degree to be populated.
• A (numpy 5D, rank-1 array) - The full alignment tensor in {Axx, Ayy, Axy, Axz, Ayz} notation.
• red_tensor (numpy 5D, rank-1 array) - The structure in {Axx, Ayy, Axy, Axz, Ayz} notation to place the reduced alignment tensor.

reduce_alignment_tensor_symmetric(D, A, red_tensor)

Calculate the reduction in the alignment tensor caused by the Frame Order matrix.

This is both the forward rotation notation and Kronecker product arrangement. This simplification is due to the symmetry in motion of the pseudo-elliptic and isotropic cones. All element of the frame order matrix where an index appears only once are zero.

Parameters:

• D (numpy 9D, rank-2 array) - The Frame Order matrix, 2nd degree to be populated.
• A (numpy 5D, rank-1 array) - The full alignment tensor in {Axx, Ayy, Axy, Axz, Ayz} notation.
• red_tensor (numpy 5D, rank-1 array) - The structure in {Axx, Ayy, Axy, Axz, Ayz} notation to place the reduced alignment tensor.

rotate_daeg(matrix, Rx2_eigen)

Rotate the given frame order matrix.

It is assumed that the frame order matrix is in the Kronecker product form.

Parameters:

• matrix (numpy 9D, rank-2 array) - The Frame Order matrix, 2nd degree to be populated.
• Rx2_eigen (numpy 9D, rank-2 array) - The Kronecker product of the eigenframe rotation matrix with itself.