meshi.util.overlap
Class Overlap

java.lang.Object
  meshi.util.overlap.Overlap

public class Overlap
extends java.lang.Object

Kabsch algorithm for optimal superposition. The following class implements the procedure for obtaining
the best rotation to relate two sets of vectors as described
in papers:
1. "A solution for the best rotation to relate two sets of vectors". By Wolfgang Kabsch, Acta Cryst. (1976) A 32: 922-923
2. "A discussion of the solution for the best rotation to relate two sets
of vectors". By Wolfgang Kabsch, Acta Cryst. (1978). A34, 827-828 .

Field Summary

private static double[][]	bvector
private static java.lang.String	comment
private static java.lang.String	comment2
private static double[][]	coor
private static double[][]	coor2
private static double[]	eigenv
private static double[][]	eigenVectors
private static double	eps
private static double[][]	help
private static int	npt
private static double	rms
private static double[][]	temp
private static double[][]	Umatrix

Constructor Summary

Overlap(double[][] co, double[][] co2, int n, java.lang.String com, java.lang.String com2)

Method Summary

static double[][]	calcBvectors() Calculating the B vectors (equation 12 at Kabsch-1976)
static double[]	calcCharPol(double[][] mat) this function will calculate the characteristic polynom after caululating the determinant manually
static void	calculateRms()
static void	checkEigenval(double[] eigenval) We now have to find the corresponding eigenvectors so we check if all eigenvalues are different or not.
static void	checkEigenVec() In order to get the proper rotation matrix (kabsch 1978) when a1,a2,a3 are out eigenvectors we make sure that a1*a2 = a3
static double[][]	copyMat(double[][] mat)
static double[][]	createP() Building a P matrix according to equation 10 which is R*Rt(1976)
static double[][]	createR() Building the R matrix according to equation 7 at the Kabsch paper (1976)
static void	createUmatrix(double[][] bVectors) Creating the U matrix, the rotation matrix.
static double[]	findEigenval(double[] charpol) In order to find the 3 eigenValues of P, which is a positive definite matrix, we are solving a cubic equation
static double[][]	findEigenvec1(double[] eigenval) Incase all 3 eigenvalues are different (most cases) in order to derive the eigenvectors we use the Gauss elimination procedure with scaled pivoting
static double[][]	findEigenvec2(double[] eigenval) FIND EIGEN VEC 2
static double	findMax(double a, double b)
static double	findMaxAbs(double a, double b) some help functions
static double	findMin(double a, double b)
static void	gravityCenter() Uniting the gravity center of both proteins to (0,0,0)
private static void	initiateFields(double[][] co, double[][] co2, int n, java.lang.String com, java.lang.String com2) A function that initializes all the class fields so that all the other functions can use them
double	rms()
static double	rmsPartial(double[][] co, double[][] co2, int[] partList) Finds the RMS according to a small subset of the two proteins.
static double	rmsPartialAltRMS(double[][] co, double[][] co2, int[] partList) This is exactly the same as 'rmsPartial' except that the rms is calculated on the subset only.
double[][]	rotationMatrix()
private static double[]	sortEigenval(double[] eigenval) this function sorts the eigenvalues in descending order, according to Kabsch(1978) so we obtain the proper rotation matrix

Methods inherited from class java.lang.Object

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

Field Detail

coor

private static double[][] coor

coor2

private static double[][] coor2

temp

private static double[][] temp

comment

private static java.lang.String comment

comment2

private static java.lang.String comment2

npt

private static int npt

help

private static double[][] help

eigenv

private static double[] eigenv

eigenVectors

private static double[][] eigenVectors

bvector

private static double[][] bvector

Umatrix

private static double[][] Umatrix

eps

private static double eps

rms

private static double rms

Constructor Detail

Overlap

public Overlap(double[][] co,
               double[][] co2,
               int n,
               java.lang.String com,
               java.lang.String com2)

Method Detail

rotationMatrix

public double[][] rotationMatrix()

rms

public double rms()

initiateFields

private static void initiateFields(double[][] co,
                                   double[][] co2,
                                   int n,
                                   java.lang.String com,
                                   java.lang.String com2)

A function that initializes all the class fields so that
all the other functions can use them

gravityCenter

public static void gravityCenter()

Uniting the gravity center of both proteins to (0,0,0)

createR

public static double[][] createR()

Building the R matrix according to equation 7
at the Kabsch paper (1976)

createP

public static double[][] createP()

Building a P matrix according to equation 10
which is R*Rt(1976)

calcCharPol

public static double[] calcCharPol(double[][] mat)

this function will calculate the characteristic polynom after caululating the determinant manually

findEigenval

public static double[] findEigenval(double[] charpol)

In order to find the 3 eigenValues of P, which is
a positive definite matrix, we are solving a cubic equation

sortEigenval

private static double[] sortEigenval(double[] eigenval)

this function sorts the eigenvalues in descending order, according to Kabsch(1978) so we obtain the proper rotation matrix

checkEigenval

public static void checkEigenval(double[] eigenval)

We now have to find the corresponding eigenvectors so we check if all eigenvalues are different or not. Then sending the eigenvalues to a function that calculates the vectors

findEigenvec1

public static double[][] findEigenvec1(double[] eigenval)

Incase all 3 eigenvalues are different (most cases) in order to derive the eigenvectors we use the Gauss elimination procedure with scaled pivoting

findEigenvec2

public static double[][] findEigenvec2(double[] eigenval)

FIND EIGEN VEC 2

checkEigenVec

public static void checkEigenVec()

In order to get the proper rotation matrix (kabsch 1978) when a1,a2,a3 are out eigenvectors we make sure that a1*a2 = a3

calcBvectors

public static double[][] calcBvectors()

Calculating the B vectors (equation 12 at Kabsch-1976)

createUmatrix

public static void createUmatrix(double[][] bVectors)

Creating the U matrix, the rotation matrix. Please note that since we switched the X and the Y atoms when creating the R matrix, we don't return U but the transposed of U

calculateRms

public static void calculateRms()

findMaxAbs

public static double findMaxAbs(double a,
                                double b)

some help functions

findMin

public static double findMin(double a,
                             double b)

findMax

public static double findMax(double a,
                             double b)

copyMat

public static double[][] copyMat(double[][] mat)

rmsPartial

public static double rmsPartial(double[][] co,
                                double[][] co2,
                                int[] partList)

Finds the RMS according to a small subset of the two proteins. The subset is an array of indexes to set of atoms in the proteins (starting from 0 for the first atom).The second protein is then rotated so that the subset is in best rms fit woth the first protein. the first protein does not move. The output RMS number is the RMS of the entire two proteins.

rmsPartialAltRMS

public static double rmsPartialAltRMS(double[][] co,
                                      double[][] co2,
                                      int[] partList)

This is exactly the same as 'rmsPartial' except that the rms is calculated on the subset only.