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# Module superimpose

source code

Module for handling all types of structural superimpositions.

 Functions
numpy rank-1, 3D array
 find_centroid(coords) Calculate the centroid of the structural coordinates. source code
list of numpy rank-1 3D arrays, list of numpy rank-2 3D arrays, list of numpy rank-1 3D arrays
 fit_to_first(models=None, coord=None, centre_type=`'``centroid``'`, elements=None, centroid=None) Superimpose a set of structural models using the fit to first algorithm. source code
list of numpy rank-1 3D arrays, list of numpy rank-2 3D arrays, list of numpy rank-1 3D arrays
 fit_to_mean(models=None, coord=None, centre_type=`'``centroid``'`, elements=None, centroid=None, verbosity=1) Superimpose a set of structural models using the fit to first algorithm. source code
numpy rank-1 3D array, float, numpy rank-2 3D array, numpy rank-1 3D array, float, numpy rank-1 3D array
 kabsch(name_from=None, name_to=None, coord_from=None, coord_to=None, centre_type=`'``centroid``'`, elements=None, centroid=None, verbosity=1) Calculate the rotational and translational displacements between the two given coordinate sets. source code
numpy rank-2, 3D array
 kabsch_rotation(coord_from=None, coord_to=None, centroid_from=None, centroid_to=None) Calculate the rotation via SVD. source code
 Variables
__package__ = `'lib.structure'`

Imports: deepcopy, pi, diag, dot, eye, float64, outer, sign, transpose, zeros, det, norm, svd, centre_of_mass, calc_mean_structure, R_to_axis_angle, R_to_euler_zyz

 Function Details

### find_centroid(coords)

source code

Calculate the centroid of the structural coordinates.

Parameters:
• `coord` (numpy rank-2, Nx3 array) - The atomic coordinates.
Returns: numpy rank-1, 3D array
The centroid.

### fit_to_first(models=None, coord=None, centre_type=`'``centroid``'`, elements=None, centroid=None)

source code

Superimpose a set of structural models using the fit to first algorithm.

Parameters:
• `models` (list of int) - The list of models to superimpose.
• `coord` (list of numpy rank-2, Nx3 arrays) - The list of coordinates of all models to superimpose. The first index is the models, the second is the atomic positions, and the third is the xyz coordinates.
• `centroid` (list of float or numpy rank-1, 3D array) - An alternative position of the centroid to allow for different superpositions, for example of pivot point motions.
• `centre_type` (str) - The type of centre to superimpose over. This can either be the standard centroid superimposition or the CoM could be used instead.
• `elements` (list of str) - The list of elements corresponding to the atoms.
Returns: list of numpy rank-1 3D arrays, list of numpy rank-2 3D arrays, list of numpy rank-1 3D arrays
The lists of translation vectors, rotation matrices, and rotation pivots.

### fit_to_mean(models=None, coord=None, centre_type=`'``centroid``'`, elements=None, centroid=None, verbosity=1)

source code

Superimpose a set of structural models using the fit to first algorithm.

Parameters:
• `models` (list of int) - The list of models to superimpose.
• `coord` (list of numpy rank-2, Nx3 arrays) - The list of coordinates of all models to superimpose. The first index is the models, the second is the atomic positions, and the third is the xyz coordinates.
• `centre_type` (str) - The type of centre to superimpose over. This can either be the standard centroid superimposition or the CoM could be used instead.
• `elements` (list of str) - The list of elements corresponding to the atoms.
• `centroid` (list of float or numpy rank-1, 3D array) - An alternative position of the centroid to allow for different superpositions, for example of pivot point motions.
• `verbosity` (int) - The amount of information to print out. If 0, nothing will be printed.
Returns: list of numpy rank-1 3D arrays, list of numpy rank-2 3D arrays, list of numpy rank-1 3D arrays
The lists of translation vectors, rotation matrices, and rotation pivots.

### kabsch(name_from=None, name_to=None, coord_from=None, coord_to=None, centre_type=`'``centroid``'`, elements=None, centroid=None, verbosity=1)

source code

Calculate the rotational and translational displacements between the two given coordinate sets.

This uses the Kabsch algorithm.

Parameters:
• `name_from` (str) - The name of the starting structure, used for the printouts.
• `name_to` (str) - The name of the ending structure, used for the printouts.
• `coord_from` (numpy rank-2, Nx3 array) - The list of atomic coordinates for the starting structure.
• `coord_to` (numpy rank-2, Nx3 array) - The list of atomic coordinates for the ending structure.
• `centre_type` (str) - The type of centre to superimpose over. This can either be the standard centroid superimposition or the CoM could be used instead.
• `elements` (list of str) - The list of elements corresponding to the atoms.
• `centroid` (list of float or numpy rank-1, 3D array) - An alternative position of the centroid, used for studying pivoted systems.
Returns: numpy rank-1 3D array, float, numpy rank-2 3D array, numpy rank-1 3D array, float, numpy rank-1 3D array
The translation vector T, translation distance d, rotation matrix R, rotation axis r, rotation angle theta, and the rotational pivot defined as the centroid of the ending structure.

### kabsch_rotation(coord_from=None, coord_to=None, centroid_from=None, centroid_to=None)

source code

Calculate the rotation via SVD.

Parameters:
• `coord_from` (numpy rank-2, Nx3 array) - The list of atomic coordinates for the starting structure.
• `coord_to` (numpy rank-2, Nx3 array) - The list of atomic coordinates for the ending structure.
• `centroid_from` (numpy rank-1, 3D array) - The starting centroid.
• `centroid_to` (numpy rank-1, 3D array) - The ending centroid.
Returns: numpy rank-2, 3D array
The rotation matrix.

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