com.numericalmethod.suanshu.matrix.doubles.factorization.eigen.qr

Class Hessenberg.Deflation

java.lang.Object

com.numericalmethod.suanshu.matrix.doubles.factorization.eigen.qr.Hessenberg.Deflation

All Implemented Interfaces:

java.io.Serializable

Enclosing class:

Hessenberg

public static class Hessenberg.Deflation
extends java.lang.Object
implements java.io.Serializable

This class encapsulates the indices for the upper left hand corner and lower right hand corner of H₂₂ as a result of the deflation procedure. Given a Hessenberg matrix, \[ \begin{bmatrix} H_{11} & H_{12} & H_{13}\\ 0 & H_{22} & H_{23}\\ 0 & 0 & H_{33} \end{bmatrix} \]

• \(u_l\) is the upper left hand corner index of H₂₂;
• \(l_r\) is the lower right hand corner index of H₂₂

If both \(u_l\) and \(l_r\) are all zeros, it means that H is a quasi-triangular matrix.

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
boolean	isQuasiTriangular true if the matrix is a quasi-triangular matrix
int	lr H33 an upper quasi-triangular in Algorithm 7.5.2 has dimension \((n-l_r) \times (n-l_r)\).
int	ul H22 an unreduced Hessenberg in Algorithm 7.5.2 has the dimension \((l_r-r_l+1) \times (l_r-u_l+1)\).

Method Summary

Methods inherited from class java.lang.Object

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

Field Detail

ul

public final int ul

H22 an unreduced Hessenberg in Algorithm 7.5.2 has the dimension \((l_r-r_l+1) \times (l_r-u_l+1)\). We try to minimize \(u_l\) (hence maximize the H₂₂ dimension).

lr

public final int lr

H33 an upper quasi-triangular in Algorithm 7.5.2 has dimension \((n-l_r) \times (n-l_r)\). We try to minimize \(l_r\) (hence maximize the H₃₃ dimension).

isQuasiTriangular

public final boolean isQuasiTriangular

true if the matrix is a quasi-triangular matrix