org.biojava.nbio.structure.geometry

Class SuperPositionQCP

java.lang.Object

org.biojava.nbio.structure.geometry.SuperPositionQCP

public final class SuperPositionQCP
extends Object

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() Default constructor
SuperPositionQCP(boolean centered) Constructor with option to set centered flag.

Method Summary

Modifier and Type	Method and Description
double	getRmsd() Return the RMSD of the superposition of input coordinate set y onto x.
javax.vecmath.Matrix3d	getRotationMatrix()
javax.vecmath.Matrix4d	getTransformationMatrix() Returns a 4x4 transformation matrix that transforms the y coordinates onto the x coordinates.
javax.vecmath.Point3d[]	getTransformedCoordinates() Returns the transformed (superposed) y coordinates TODO this is actually returning a transformation of the x coordinates, we should review if that's correct and change it if not
void	set(javax.vecmath.Point3d[] x, javax.vecmath.Point3d[] y) Sets the two input coordinate arrays.
void	set(javax.vecmath.Point3d[] x, javax.vecmath.Point3d[] y, double[] weight) Sets the two input coordinate arrays and weight array.
void	setCentered(boolean centered)

Methods inherited from class java.lang.Object

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

Constructor Detail

SuperPositionQCP

public SuperPositionQCP()

Default constructor

SuperPositionQCP

public SuperPositionQCP(boolean centered)

Constructor with option to set centered flag. This constructor should be used if both coordinate input set have been centered at the origin.

Parameters:

centered - if set true, the input coordinates are already centered at the origin

Method Detail

set

public void set(javax.vecmath.Point3d[] x,
                javax.vecmath.Point3d[] y)

Sets the two input coordinate arrays. These input arrays must be of equal length. Input coordinates are not modified.

Parameters:

x - 3d points of reference coordinate set

y - 3d points of coordinate set for superposition

set

public void set(javax.vecmath.Point3d[] x,
                javax.vecmath.Point3d[] y,
                double[] weight)

Sets the two input coordinate arrays and weight array. All input arrays must be of equal length. Input coordinates are not modified.

Parameters:

x - 3d points of reference coordinate set

y - 3d points of coordinate set for superposition

weight - a weight in the inclusive range [0,1] for each point

setCentered

public void setCentered(boolean centered)

getRmsd

public double getRmsd()

Return the RMSD of the superposition of input coordinate set y onto x. Note, this is the fasted way to calculate an RMSD without actually superposing the two sets. The calculation is performed "lazy", meaning calculations are only performed if necessary.

Returns:

root mean square deviation for superposition of y onto x

getTransformationMatrix

public javax.vecmath.Matrix4d getTransformationMatrix()

Returns a 4x4 transformation matrix that transforms the y coordinates onto the x coordinates. The calculation is performed "lazy", meaning calculations are only performed if necessary.

Returns:

4x4 transformation matrix to transform y coordinates onto x

getRotationMatrix

public javax.vecmath.Matrix3d getRotationMatrix()

getTransformedCoordinates

public javax.vecmath.Point3d[] getTransformedCoordinates()

Returns the transformed (superposed) y coordinates TODO this is actually returning a transformation of the x coordinates, we should review if that's correct and change it if not

Returns:

transformed y coordinates