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

java.lang.Object
  com.numericalmethod.suanshu.matrix.doubles.factorization.eigen.Hessenberg.Deflation

Enclosing class:

Hessenberg

public static class Hessenberg.Deflation
extends java.lang.Object

This class encapsulates the indices for the upper left hand corner, and lower right hand corner of H22.

Given a Hessenberg matrix,

     | H11 H12 H13 |
 H = | 0   H22 H23 |
     | 0   0   H33 |
 

• ul is the upper left hand corner index of H22
• lr is the lower right hand corner index of H22

If both ul and lr are all zeros, it means that H is a quasi-triangular matrix.

Field Summary

boolean	isQuasiTriangular true iff the matrix is a quasi-triangular matrix
int	lr H33, upper quasi-triangular, in Algorithm 7.5.2 has dimension (n-lr) x (n-lr).
int	ul H22, unreduced Hessenberg, in Algorithm 7.5.2 has dimension (lr-ul+1) x (lr-ul+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, unreduced Hessenberg, in Algorithm 7.5.2 has dimension

(lr-ul+1) x (lr-ul+1)

.

We try to minimize ul (maximize H22 dim).

lr

public final int lr

H33, upper quasi-triangular, in Algorithm 7.5.2 has dimension

(n-lr) x (n-lr)

.

We try to minimize lr (maximize H33 dim).

isQuasiTriangular

public final boolean isQuasiTriangular

true iff the matrix is a quasi-triangular matrix