org.biojava.nbio.structure.geometry

Class SuperPositionQCP

java.lang.Object

org.biojava.nbio.structure.geometry.SuperPositionAbstract

org.biojava.nbio.structure.geometry.SuperPositionQCP

All Implemented Interfaces:

SuperPosition

public final class SuperPositionQCP
extends SuperPositionAbstract

Implementation of the Quaternion-Based Characteristic Polynomial algorithm for RMSD and Superposition calculations.

Usage:

The input consists of 2 Point3d arrays of equal length. The input coordinates are not changed.

    Point3d[] x = ...
    Point3d[] y = ...
    SuperPositionQCP qcp = new SuperPositionQCP();
    qcp.set(x, y);
 

or with weighting factors [0 - 1]]

    double[] weights = ...
    qcp.set(x, y, weights);
 

For maximum efficiency, create a SuperPositionQCP object once and reuse it.

A. Calculate rmsd only

 double rmsd = qcp.getRmsd();
 

B. Calculate a 4x4 transformation (rotation and translation) matrix

 Matrix4d rottrans = qcp.getTransformationMatrix();
 

C. Get transformated points (y superposed onto the reference x)

 Point3d[] ySuperposed = qcp.getTransformedCoordinates();
 

Citations:

Liu P, Agrafiotis DK, & Theobald DL (2011) Reply to comment on: "Fast determination of the optimal rotation matrix for macromolecular superpositions." Journal of Computational Chemistry 32(1):185-186. [http://dx.doi.org/10.1002/jcc.21606]

Liu P, Agrafiotis DK, & Theobald DL (2010) "Fast determination of the optimal rotation matrix for macromolecular superpositions." Journal of Computational Chemistry 31(7):1561-1563. [http://dx.doi.org/10.1002/jcc.21439]

Douglas L Theobald (2005) "Rapid calculation of RMSDs using a quaternion-based characteristic polynomial." Acta Crystallogr A 61(4):478-480. [http://dx.doi.org/10.1107/S0108767305015266 ]

This is an adoption of the original C code QCProt 1.4 (2012, October 10) to Java. The original C source code is available from http://theobald.brandeis.edu/qcp/ and was developed by

Douglas L. Theobald Department of Biochemistry MS 009 Brandeis University 415 South St Waltham, MA 02453 USA

dtheobald@brandeis.edu

Pu Liu Johnson & Johnson Pharmaceutical Research and Development, L.L.C. 665 Stockton Drive Exton, PA 19341 USA

pliu24@its.jnj.com

Author:

Douglas L. Theobald (original C code), Pu Liu (original C code), Peter Rose (adopted to Java), Aleix Lafita (adopted to Java)

Constructor Summary

Constructors

Constructor and Description
SuperPositionQCP(boolean centered) Default constructor for the quaternion based superposition algorithm.
SuperPositionQCP(boolean centered, double evec_prec, double eval_prec) Constructor with option to set the precision values.

Method Summary

Modifier and Type	Method and Description
double	getRmsd(javax.vecmath.Point3d[] fixed, javax.vecmath.Point3d[] moved) Calculate the RMSD between two arrays of equivalent points that are not superposed.
double	getWeightedRmsd(javax.vecmath.Point3d[] fixed, javax.vecmath.Point3d[] moved, double[] weight)
javax.vecmath.Matrix4d	superpose(javax.vecmath.Point3d[] fixed, javax.vecmath.Point3d[] moved) Obtain the superposition matrix that minimizes the RMSD between two arrays of equivalent points.
javax.vecmath.Matrix4d	superposeAfterRmsd() The QCP method can be used as a two-step calculation: first compute the RMSD (fast) and then compute the superposition.
javax.vecmath.Matrix4d	weightedSuperpose(javax.vecmath.Point3d[] fixed, javax.vecmath.Point3d[] moved, double[] weight) Weighted superposition.

Methods inherited from class org.biojava.nbio.structure.geometry.SuperPositionAbstract

checkInput, setCentered, superposeAndTransform

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

SuperPositionQCP

public SuperPositionQCP(boolean centered)

Default constructor for the quaternion based superposition algorithm.

Parameters:

centered - true if the point arrays are centered at the origin (faster), false otherwise

SuperPositionQCP

public SuperPositionQCP(boolean centered,
                        double evec_prec,
                        double eval_prec)

Constructor with option to set the precision values.

Parameters:

centered - true if the point arrays are centered at the origin (faster), false otherwise

evec_prec - required eigenvector precision

eval_prec - required eigenvalue precision

Method Detail

weightedSuperpose

public javax.vecmath.Matrix4d weightedSuperpose(javax.vecmath.Point3d[] fixed,
                                                javax.vecmath.Point3d[] moved,
                                                double[] weight)

Weighted superposition.

Parameters:

fixed -

moved -

weight - array of weigths for each equivalent point position

Returns:

getRmsd

public double getRmsd(javax.vecmath.Point3d[] fixed,
                      javax.vecmath.Point3d[] moved)

Description copied from interface: SuperPosition

Calculate the RMSD between two arrays of equivalent points that are not superposed.

This is equivalent to first superposing the point arrays with SuperPosition.superposeAndTransform(Point3d[], Point3d[]) and then calculating the RMSD of the superposed point arrays with CalcPoint.rmsd(Point3d[], Point3d[]), but it will be faster when the transformation matrix is not needed.

The two point arrays have to be of the same length and the order of points have to be the same, so that a specific position in the one array is equivalent to the same position in the other array.

Parameters:

fixed - an array of points. Original coordinates will not be modified.

moved - an array of points. Original coordinates will not be modified.

Returns:

the minimum RMSD between the equivalent point arrays (after superposition)

superpose

public javax.vecmath.Matrix4d superpose(javax.vecmath.Point3d[] fixed,
                                        javax.vecmath.Point3d[] moved)

Description copied from interface: SuperPosition

Obtain the superposition matrix that minimizes the RMSD between two arrays of equivalent points.

The two point arrays have to be of the same length and the order of points have to be the same, so that a specific position in the one array is equivalent to the same position in the other array.

Parameters:

fixed - point array as reference, onto which the other point array is superposed. Original coordinates will not be modified.

moved - point array to which the resulting transformation matrix is applied. Original coordinates will not be modified.

Returns:

transformation matrix as a Matrix4d to superpose moved onto fixed point arrays

getWeightedRmsd

public double getWeightedRmsd(javax.vecmath.Point3d[] fixed,
                              javax.vecmath.Point3d[] moved,
                              double[] weight)

Parameters:

fixed -

moved -

weight - array of weigths for each equivalent point position

Returns:

weighted RMSD.

superposeAfterRmsd

public javax.vecmath.Matrix4d superposeAfterRmsd()

The QCP method can be used as a two-step calculation: first compute the RMSD (fast) and then compute the superposition. This method assumes that the RMSD of two arrays of points has been already calculated using getRmsd(Point3d[], Point3d[]) method and calculates the transformation of the same two point arrays.

Parameters:

fixed -

moved -

Returns:

transformation matrix as a Matrix4d to superpose moved onto fixed point arrays