NAME

SRC/slaqz3.f

SYNOPSIS

Functions/Subroutines

recursive subroutine slaqz3 (ilschur, ilq, ilz, n, ilo, ihi, nw, a, lda, b, ldb, q, ldq, z, ldz, ns, nd, alphar, alphai, beta, qc, ldqc, zc, ldzc, work, lwork, rec, info)
SLAQZ3

Function/Subroutine Documentation

recursive subroutine slaqz3 (logical, intent(in) ilschur, logical, intent(in) ilq, logical, intent(in) ilz, integer, intent(in) n, integer, intent(in) ilo, integer, intent(in) ihi, integer, intent(in) nw, real, dimension( lda, * ), intent(inout) a, integer, intent(in) lda, real, dimension( ldb, * ), intent(inout) b, integer, intent(in) ldb, real, dimension( ldq, * ), intent(inout) q, integer, intent(in) ldq, real, dimension( ldz, * ), intent(inout) z, integer, intent(in) ldz, integer, intent(out) ns, integer, intent(out) nd, real, dimension( * ), intent(inout) alphar, real, dimension( * ), intent(inout) alphai, real, dimension( * ), intent(inout) beta, real, dimension( ldqc, * ) qc, integer, intent(in) ldqc, real, dimension( ldzc, * ) zc, integer, intent(in) ldzc, real, dimension( * ) work, integer, intent(in) lwork, integer, intent(in) rec, integer, intent(out) info)

SLAQZ3

Purpose:



 SLAQZ3 performs AED

Parameters

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 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 is INTEGER


          The desired size of the deflation window.



          A is REAL array, dimension (LDA, N)

LDA



          LDA is INTEGER


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



          B is REAL array, dimension (LDB, N)

LDB



          LDB is INTEGER


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



          Q is REAL array, dimension (LDQ, N)

LDQ



          LDQ is INTEGER



          Z is REAL array, dimension (LDZ, N)

LDZ



          LDZ is INTEGER



          NS is INTEGER


          The number of unconverged eigenvalues available to


          use as shifts.



          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 is REAL array, dimension (LDQC, NW)

LDQC



          LDQC is INTEGER



          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

Author

Thijs Steel, KU Leuven

Date

May 2020

Definition at line 234 of file slaqz3.f.

Author

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