# SuanShu, a Java numerical and statistical library

com.numericalmethod.suanshu.algebra.linear.matrix.doubles.factorization.eigen.mr3.getvec

## Class Getvec

• java.lang.Object
• com.numericalmethod.suanshu.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 = LDLT - λ I. This is essentially Algorithm Getvec.

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

• "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

All Methods
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 LDLT
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()