kabsch: Kabsch Algorithm

In KODAMA: Knowledge Discovery by Accuracy Maximization

Kabsch Algorithm

Description

Aligns two sets of points via rotations and translations. Given two sets of points, with one specified as the reference set, the other set will be rotated so that the RMSD between the two is minimized. The format of the matrix is that there should be one row for each of n observations, and the number of columns, d, specifies the dimensionality of the points. The point sets must be of equal size and with the same ordering, i.e. point one of the second matrix is mapped to point one of the reference matrix, point two of the second matrix is mapped to point two of the reference matrix, and so on.

Usage

kabsch (pm, qm)

Arguments

pm	n x d matrix of points to align to to qm.
qm	n x d matrix of reference points.

Value

Matrix pm rotated and translated so that the ith point is aligned to the ith point of qm in the least-squares sense.

Author(s)

James Melville

Examples

data=iris[,-5]
pp1=pca(data)$x
pp2=pca(scale(data))$x
pp3=kabsch(pp1,pp2)
plot(pp1,pch=21,bg=rep(2:4,each=50))
points(pp3,pch=21,bg=rep(2:4,each=50),col=5)

KODAMA documentation built on June 8, 2025, 11:53 a.m.