dev.nm.algebra.linear.matrix.doubles.factorization.eigen.mr3.getvec

Class Getvec

java.lang.Object

dev.nm.algebra.linear.matrix.doubles.factorization.eigen.mr3.getvec.Getvec

public class Getvec
extends Object

Computes the (scaled) r-th column of the inverse of the sub-matrix block of the tridiagonal matrix \(T = LDL^{\mathsf T} - \lambda I\). This is essentially Algorithm Getvec.

This is used to compute an Fernando and Parlett (FP) vector of a singleton in MRRR.

See Also:

• "Dhillon, Inderjit S. and Parlett, Beresford N., "Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices", Linear Algebra and its Applications, 2004, 387, pp. 1-28."
• "Dhillon, Inderjit S. and Parlett, Beresford N., "Orthogonal eigenvectors and relative gaps", SIAM Journal on Matrix Analysis and Applications, 2004, Vol. 25, pp. 858-899."

Constructor Summary

Constructors

Constructor and Description
Getvec(LDDecomposition LDLt, double lambda, int twistIndex, double gapTolerance, double minPivot) Computes an FP vector of a singleton.

Method Summary

Modifier and Type	Method and Description
Vector	getEigenvector()
int	getFirstNonZeroIndex()
double	getInverseNorm()
int	getLastNonZeroIndex()
int	getNegCount()
double	getResidual()
double	getRQCorrection()
int	getTwistIndex()

Methods inherited from class java.lang.Object

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

Constructor Detail

Getvec

public Getvec(LDDecomposition LDLt,
              double lambda,
              int twistIndex,
              double gapTolerance,
              double minPivot)

Computes an FP vector of a singleton.

Parameters:

LDLt - the robust representation \(LDL^{\mathsf T}\)

lambda - the shift λ

twistIndex - the twist index r

gapTolerance - the gap tolerance

minPivot - the minimum pivot in the Sturm sequence for T

Method Detail

getNegCount

public int getNegCount()

getTwistIndex

public int getTwistIndex()

getInverseNorm

public double getInverseNorm()

getResidual

public double getResidual()

getRQCorrection

public double getRQCorrection()

getFirstNonZeroIndex

public int getFirstNonZeroIndex()

getLastNonZeroIndex

public int getLastNonZeroIndex()

getEigenvector

public Vector getEigenvector()