Package gov.nih.mipav.model.algorithms

Class Kabsch

java.lang.Object

gov.nih.mipav.model.algorithms.Kabsch

public class Kabsch
extends java.lang.Object

Copyright (c) 2009, Ehud Schreiber All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. % Find the Least Root Mean Square distance % between two sets of N points in D dimensions % and the rigid transformation (i.e. translation and rotation) % to employ in order to bring one set that close to the other, % Using the Kabsch (1976) algorithm. % Note that the points are paired, i.e. we know which point in one set % should be compared to a given point in the other set. % % References: % 1) Kabsch W. A solution for the best rotation to relate two sets of vectors. Acta Cryst A 1976;32:9223. % 2) Kabsch W. A discussion of the solution for the best rotation to relate two sets of vectors. Acta Cryst A 1978;34:8278. % 3) http://en.wikipedia.org/wiki/Kabsch_algorithm % % We slightly generalize, allowing weights given to the points. % Those weights are determined a priori and do not depend on the distances. % % We work in the convention that points are column vectors; % some use the convention where they are row vectors instead. % % Input variables: % P : a D*N matrix where P(a,i) is the a-th coordinate of the i-th point % in the 1st representation % Q : a D*N matrix where Q(a,i) is the a-th coordinate of the i-th point % in the 2nd representation % m : (Optional) a row vector of length N giving the weights, i.e. m(i) is % the weight to be assigned to the deviation of the i-th point. % If not supplied, we take by default the unweighted (or equal weighted) % m(i) = 1/N. % The weights do not have to be normalized; % we divide by the sum to ensure sum_{i=1}^N m(i) = 1. % The weights must be non-negative with at least one positive entry. % Output variables: % U : a proper orthogonal D*D matrix, representing the rotation % r : a D-dimensional column vector, representing the translation % lrms: the Least Root Mean Square % % Details: % If p_i, q_i are the i-th point (as a D-dimensional column vector) % in the two representations, i.e. p_i = P(:,i) etc., and for % p_i' = U p_i + r (' does not stand for transpose!) % we have p_i' ~ q_i, that is, % lrms = sqrt(sum_{i=1}^N m(i) (p_i' - q_i)^2) % is the minimal rms when going over the possible U and r. % (assuming the weights are already normalized). %

Field Summary

Fields

Modifier and Type	Field	Description
(package private) double[]	lrms
(package private) double[]	m
(package private) double[][]	P
(package private) double[][]	Q
(package private) double[]	r
(package private) double[][]	U

Constructor Summary

Constructors

Constructor	Description
Kabsch()
Kabsch(double[][] U, double[] r, double[] lrms, double[][] P, double[][] Q, double[] m)

Method Summary

Modifier and Type	Method	Description
void	run()
void	selfTest()

Methods inherited from class java.lang.Object

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

Field Detail

P

double[][] P

Q

double[][] Q

m

double[] m

U

double[][] U

r

double[] r

lrms

double[] lrms

Constructor Detail

Kabsch

public Kabsch()

Kabsch

public Kabsch(double[][] U,
              double[] r,
              double[] lrms,
              double[][] P,
              double[][] Q,
              double[] m)

Method Detail

selfTest

public void selfTest()

run

public void run()