## Class SuperPositionSVD

• All Implemented Interfaces:
`SuperPosition`

```public class SuperPositionSVD
extends SuperPositionAbstract```
A class that calculates the superposition between two sets of points using an SVD Matrix Decomposition. It was introduced by Wolfgang Kabsch, hence the alternative name Kabsh algorithm. Inspired by the biopython SVDSuperimposer class.
Since:
1.5
Version:
%I% %G%
Author:
Andreas Prlic, Aleix Lafita

• ### Fields inherited from class org.biojava.nbio.structure.geometry.SuperPositionAbstract

`centered`
• ### Constructor Summary

Constructors
Constructor Description
`SuperPositionSVD​(boolean centered)`
Constructor for the SVD superposition algorithm.
• ### Method Summary

All Methods
Modifier and Type Method Description
`double` ```getRmsd​(javax.vecmath.Point3d[] x, javax.vecmath.Point3d[] y)```
Calculate the RMSD between two arrays of equivalent points that are not superposed.
`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.
• ### 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

• #### SuperPositionSVD

`public SuperPositionSVD​(boolean centered)`
Constructor for the SVD superposition algorithm.
Parameters:
`centered` - true if the point arrays are centered at the origin (faster), false otherwise
• ### Method Detail

• #### 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
• #### getRmsd

```public double getRmsd​(javax.vecmath.Point3d[] x,
javax.vecmath.Point3d[] y)```
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:
`x` - an array of points. Original coordinates will not be modified.
`y` - an array of points. Original coordinates will not be modified.
Returns:
the minimum RMSD between the equivalent point arrays (after superposition)