# 13.2.9. Fast QCP RMSD structure alignment — `MDAnalysis.lib.qcprot`

Author:

Joshua L. Adelman, University of Pittsburgh

Author:

Robert R. Delgado, Cornell University and Arizona State University

Contact:

jla65@pitt.edu

Year:

2011, 2016

Licence:

BSD

PyQCPROT is a python/cython implementation of Douglas Theobald’s QCP method for calculating the minimum RMSD between two structures [Theobald2005] and determining the optimal least-squares rotation matrix [Liu2010].

A full description of the method, along with the original C implementation can be found at http://theobald.brandeis.edu/qcp/

Changed in version 0.16.0: Call signatures were changed to directly interface with MDAnalysis coordinate arrays: shape (N, 3)

References

If you use this QCP rotation calculation method in a publication, please reference:

Douglas L. Theobald (2005) “Rapid calculation of RMSD using a quaternion-based characteristic polynomial.” Acta Crystallographica A 61(4):478-480.

[Liu2010]

Pu Liu, Dmitris K. Agrafiotis, and Douglas L. Theobald (2010) “Fast determination of the optimal rotational matrix for macromolecular superpositions.” J. Comput. Chem. 31, 1561-1563.

## 13.2.9.1. Functions

Users will typically use the `CalcRMSDRotationalMatrix()` function.

MDAnalysis.lib.qcprot.CalcRMSDRotationalMatrix(ref, conf, N, rot, weights)

Calculate the RMSD & rotational matrix.

Parameters:
• ref (ndarray) – reference structure coordinates, shape (N, 3)

• conf (ndarray) – condidate structure coordinates, shape (N, 3)

• N (int) – size of the system

• rot (ndarray or None) – array to store rotation matrix. If given must be flat and shape (9,)

• weights (ndarray or None) – weights for each component

Returns:

• rmsd (float) – RMSD value

• .. versionchanged:: 0.16.0 – Array size changed from 3xN to Nx3.

• .. versionchanged:: 2.7.0 – Changed arguments to floating type, can accept either float32 or float64 inputs

MDAnalysis.lib.qcprot.InnerProduct(A, coords1, coords2, N, weight)

Calculate the inner product of two structures.

Parameters:
• A (ndarray) – result inner product array, modified in place

• coords1 (ndarray) – reference structure

• coords2 (ndarray) – candidate structure

• N (int) – size of system

• weight (ndarray or None) – used to calculate weighted inner product

Returns:

Notes

1. You MUST center the structures, coords1 and coords2, before calling this function.

2. Coordinates are stored as Nx3 arrays (as everywhere else in MDAnalysis).

Changed in version 0.16.0: Array size changed from 3xN to Nx3.

Changed in version 2.7.0: Updating to allow either float32 or float64 inputs

MDAnalysis.lib.qcprot.FastCalcRMSDAndRotation(rot, A, E0, N)

Calculate the RMSD, and/or the optimal rotation matrix.

Parameters:
• rot (ndarray or None) – result rotation matrix, modified inplace

• A (ndarray) – the inner product of two structures

• E0 (floating) – 0.5 * (G1 + G2)

• N (int) – size of the system

Returns:

rmsd – RMSD value for two structures

Return type:

double

Changed in version 0.16.0: Array sized changed from 3xN to Nx3.

Changed in version 2.7.0: Changed arguments to floating type, can accept either float32 or float64 inputs. Internally still uses double precision for QCP algorithm