Talk:Kabsch algorithm

As a mathematician I must say this article is horribly vaguely written.

The Kabsch algorithm is a method for calculating the optimal alignment of two sets of points.

Vague, but one hopes it will be defined below.

The algorithm works by calculating a matrix of multiplied components. The destination matrix, A, is a 3 × 3 matrix with x, y and z components for each side. The source is two sets of paired points, V₁ and V₂.

I'm guessing the "destination matrix" is supposed to be the algorithm's output, but I'm not sure.

"Two sets of paired points". Sets? Or tuples? Or matrices in which each row is one of the points? Does it mean "two paired sets of points" or "two sets of paired points" (what is a paired point)?

$A_{ij}=\sum _{i}V_{1i}V_{2j}$

(sum over the points and multiply components).

"Sum over points" could mean the index of summation is a variable representing points and runs through the whole set of points. But the notation suggests something else is meant. It looks as if the ij entry in the matrix is a dot product of the ith and jth points.

The formula is

: $(A^{t}A)^{1/2}A^{-1}$

Formula for what? What is this result supposed to be?

The algorithm calculates only the rotation matix.

What rotation matrix?? Nowhere has the article told us that we're trying to find a rotation.

And what does "optimal alignment" mean?

I am very good at deciphering things like this, and I can't make any sense of this. Michael Hardy 03:35, 19 July 2007 (UTC)

The external link seems much clearer. More later.... Michael Hardy 03:38, 19 July 2007 (UTC)

The algorithm as described assumes the bottom right singular value is the smallest one. Many numerical packages ensure it is. Many don't. It is not part of the definition of SVD that this is the case. So the algorithm is incorrect. Sigfpe (talk) 22:19, 24 June 2011 (UTC)

Mystery of the matrices

Any offers on what matrices P and Q might be ? — Preceding unsigned comment added by Eep1mp (talk • contribs) 12:21, 29 February 2012 (UTC)

Recurrence in introduction

In the introduction the named application of the algorithm in chem- and bioinformatics are almost redundant, as the term protein structure is a subset to molecular structure. In addition the application lies in the overlap of the strongly related disciplines chem- and bioinformatics, the differentiation doesn't make sense in this case. Maybe one can find more diverse applications. — Preceding unsigned comment added by Tmartin kl (talk • contribs) 10:35, 6 October 2015 (UTC)

"Goes back to"

"Expressing the optimal rotation matrix with a quaternion goes back to 1999" - I'm a bit skeptical about this date. "Closed Form Solution of Absolute Orientation using Unit Quaternions" by Horn in 1987 seems to be just that.

Nh2-wiki (talk) 22:45, 9 September 2016 (UTC)