!>
!> SLAQZ3 performs AED
!> 

ILSCHUR

!>          ILSCHUR is LOGICAL
!>              Determines whether or not to update the full Schur form
!> 

ILQ

!>          ILQ is LOGICAL
!>              Determines whether or not to update the matrix Q
!> 

ILZ

!>          ILZ is LOGICAL
!>              Determines whether or not to update the matrix Z
!> 

N

!>          N is INTEGER
!>          The order of the matrices A, B, Q, and Z.  N >= 0.
!> 

ILO

!>          ILO is INTEGER
!> 

IHI

!>          IHI is INTEGER
!>          ILO and IHI mark the rows and columns of (A,B) which
!>          are to be normalized
!> 

NW

!>          NW is INTEGER
!>          The desired size of the deflation window.
!> 

A

!>          A is REAL array, dimension (LDA, N)
!> 

LDA

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max( 1, N ).
!> 

B

!>          B is REAL array, dimension (LDB, N)
!> 

LDB

!>          LDB is INTEGER
!>          The leading dimension of the array B.  LDB >= max( 1, N ).
!> 

Q

!>          Q is REAL array, dimension (LDQ, N)
!> 

LDQ

!>          LDQ is INTEGER
!> 

Z

!>          Z is REAL array, dimension (LDZ, N)
!> 

LDZ

!>          LDZ is INTEGER
!> 

NS

!>          NS is INTEGER
!>          The number of unconverged eigenvalues available to
!>          use as shifts.
!> 

ND

!>          ND is INTEGER
!>          The number of converged eigenvalues found.
!> 

ALPHAR

!>          ALPHAR is REAL array, dimension (N)
!>          The real parts of each scalar alpha defining an eigenvalue
!>          of GNEP.
!> 

ALPHAI

!>          ALPHAI is REAL array, dimension (N)
!>          The imaginary parts of each scalar alpha defining an
!>          eigenvalue of GNEP.
!>          If ALPHAI(j) is zero, then the j-th eigenvalue is real; if
!>          positive, then the j-th and (j+1)-st eigenvalues are a
!>          complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j).
!> 

BETA

!>          BETA is REAL array, dimension (N)
!>          The scalars beta that define the eigenvalues of GNEP.
!>          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
!>          beta = BETA(j) represent the j-th eigenvalue of the matrix
!>          pair (A,B), in one of the forms lambda = alpha/beta or
!>          mu = beta/alpha.  Since either lambda or mu may overflow,
!>          they should not, in general, be computed.
!> 

QC

!>          QC is REAL array, dimension (LDQC, NW)
!> 

LDQC

!>          LDQC is INTEGER
!> 

ZC

!>          ZC is REAL array, dimension (LDZC, NW)
!> 

LDZC

!>          LDZ is INTEGER
!> 

WORK

!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO >= 0, WORK(1) returns the optimal LWORK.
!> 

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK.  LWORK >= max(1,N).
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!> 

REC

!>          REC is INTEGER
!>             REC indicates the current recursion level. Should be set
!>             to 0 on first call.
!> 

INFO

!>          INFO is INTEGER
!>          = 0: successful exit
!>          < 0: if INFO = -i, the i-th argument had an illegal value
!> 

Thijs Steel, KU Leuven

May 2020