SRC/slaqz3.f(3)            Library Functions Manual            SRC/slaqz3.f(3)

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

                     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

       Author
           Thijs Steel, KU Leuven

       Date
           May 2020

       Definition at line 234 of file slaqz3.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/slaqz3.f(3)