mikera.matrixx.decompose.impl.eigen

Class SymmetricQREigenHelper

java.lang.Object

mikera.matrixx.decompose.impl.eigen.SymmetricQREigenHelper

public class SymmetricQREigenHelper
extends Object

A helper class for the symmetric matrix implicit QR algorithm for eigenvalue decomposition. Performs most of the basic operations needed to extract eigenvalues and eigenvectors.

Author:

Peter Abeles

Field Summary

Fields

Modifier and Type	Field and Description
protected double[]	diag
protected EigenvalueSmall	eigenSmall
static double	EPS
protected int	lastExceptional
protected int	N
protected int	numExceptional
protected int	numSplits
protected double[]	off
protected Matrix	Q
protected Random	rand
protected int[]	splits
protected int	steps
protected int	x1
protected int	x2

Constructor Summary

Constructors

Constructor and Description
SymmetricQREigenHelper()

Method Summary

Modifier and Type	Method and Description
double	computeShift()
double	computeWilkinsonShift()
double[]	copyDiag(double[] ret)
double[]	copyEigenvalues(double[] ret)
double[]	copyOff(double[] ret)
protected void	createBulge(int x1, double p, boolean byAngle) Performs a similar transform on A-pI
protected void	createBulge2by2(int x1, double p, boolean byAngle)
protected void	eigenvalue2by2(int x1) Computes the eigenvalue of the 2 by 2 matrix.
void	exceptionalShift() Perform a shift in a random direction that is of the same magnitude as the elements in the matrix.
int	getMatrixSize()
void	incrementSteps()
void	init(double[] diag, double[] off, int numCols) Sets up and declares internal data structures.
protected boolean	isZero(int index) Checks to see if the specified off diagonal element is zero using a relative metric.
boolean	nextSplit() Tells it to process the submatrix at the next split.
protected void	performImplicitSingleStep(double lambda, boolean byAngle)
void	printMatrix()
protected void	removeBulge(int x1)
protected void	removeBulgeEnd(int x1) Rotator to remove the bulge
void	reset(int N) Sets the size of the matrix being decomposed, declares new memory if needed, and sets all helper functions to their initial value.
void	resetSteps()
void	setQ(Matrix q)
void	setSubmatrix(int x1, int x2) Sets which submatrix is being processed.
double[]	swapDiag(double[] diag) Exchanges the internal array of the diagonal elements for the provided one.
double[]	swapOff(double[] off) Exchanges the internal array of the off diagonal elements for the provided one.
protected void	updateQ(int m, int n, double c, double s)

Methods inherited from class java.lang.Object

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

Field Detail

EPS

public static double EPS

rand

protected Random rand

steps

protected int steps

numExceptional

protected int numExceptional

lastExceptional

protected int lastExceptional

eigenSmall

protected EigenvalueSmall eigenSmall

Q

protected Matrix Q

N

protected int N

diag

protected double[] diag

off

protected double[] off

x1

protected int x1

x2

protected int x2

splits

protected int[] splits

numSplits

protected int numSplits

Constructor Detail

SymmetricQREigenHelper

public SymmetricQREigenHelper()

Method Detail

printMatrix

public void printMatrix()

setQ

public void setQ(Matrix q)

incrementSteps

public void incrementSteps()

init

public void init(double[] diag,
                 double[] off,
                 int numCols)

Sets up and declares internal data structures.

Parameters:

diag - Diagonal elements from tridiagonal matrix. Modified.

off - Off diagonal elements from tridiagonal matrix. Modified.

numCols - number of columns (and rows) in the matrix.

swapDiag

public double[] swapDiag(double[] diag)

Exchanges the internal array of the diagonal elements for the provided one.

swapOff

public double[] swapOff(double[] off)

Exchanges the internal array of the off diagonal elements for the provided one.

reset

public void reset(int N)

Sets the size of the matrix being decomposed, declares new memory if needed, and sets all helper functions to their initial value.

copyDiag

public double[] copyDiag(double[] ret)

copyOff

public double[] copyOff(double[] ret)

copyEigenvalues

public double[] copyEigenvalues(double[] ret)

setSubmatrix

public void setSubmatrix(int x1,
                         int x2)

Sets which submatrix is being processed.

Parameters:

x1 - Lower bound, inclusive.

x2 - Upper bound, inclusive.

isZero

protected boolean isZero(int index)

Checks to see if the specified off diagonal element is zero using a relative metric.

performImplicitSingleStep

protected void performImplicitSingleStep(double lambda,
                                         boolean byAngle)

updateQ

protected void updateQ(int m,
                       int n,
                       double c,
                       double s)

createBulge

protected void createBulge(int x1,
                           double p,
                           boolean byAngle)

Performs a similar transform on A-pI

createBulge2by2

protected void createBulge2by2(int x1,
                               double p,
                               boolean byAngle)

removeBulge

protected void removeBulge(int x1)

removeBulgeEnd

protected void removeBulgeEnd(int x1)

Rotator to remove the bulge

eigenvalue2by2

protected void eigenvalue2by2(int x1)

Computes the eigenvalue of the 2 by 2 matrix.

exceptionalShift

public void exceptionalShift()

Perform a shift in a random direction that is of the same magnitude as the elements in the matrix.

nextSplit

public boolean nextSplit()

Tells it to process the submatrix at the next split. Should be called after the current submatrix has been processed.

computeShift

public double computeShift()

computeWilkinsonShift

public double computeWilkinsonShift()

getMatrixSize

public int getMatrixSize()

resetSteps

public void resetSteps()