This routine is deprecated and has been replaced by routine ZGGES.


 ZGEGS computes the eigenvalues, Schur form, and, optionally, the


 left and or/right Schur vectors of a complex matrix pair (A,B).


 Given two square matrices A and B, the generalized Schur


 factorization has the form


 


    A = Q*S*Z**H,  B = Q*T*Z**H


 


 where Q and Z are unitary matrices and S and T are upper triangular.


 The columns of Q are the left Schur vectors


 and the columns of Z are the right Schur vectors.


 


 If only the eigenvalues of (A,B) are needed, the driver routine


 ZGEGV should be used instead.  See ZGEGV for a description of the


 eigenvalues of the generalized nonsymmetric eigenvalue problem


 (GNEP).

JOBVSL

          JOBVSL is CHARACTER*1


          = 'N':  do not compute the left Schur vectors;


          = 'V':  compute the left Schur vectors (returned in VSL).

JOBVSR

          JOBVSR is CHARACTER*1


          = 'N':  do not compute the right Schur vectors;


          = 'V':  compute the right Schur vectors (returned in VSR).

N

          N is INTEGER


          The order of the matrices A, B, VSL, and VSR.  N >= 0.

A

          A is COMPLEX*16 array, dimension (LDA, N)


          On entry, the matrix A.


          On exit, the upper triangular matrix S from the generalized


          Schur factorization.

LDA

          LDA is INTEGER


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

B

          B is COMPLEX*16 array, dimension (LDB, N)


          On entry, the matrix B.


          On exit, the upper triangular matrix T from the generalized


          Schur factorization.

LDB

          LDB is INTEGER


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

ALPHA

          ALPHA is COMPLEX*16 array, dimension (N)


          The complex scalars alpha that define the eigenvalues of


          GNEP.  ALPHA(j) = S(j,j), the diagonal element of the Schur


          form of A.

BETA

          BETA is COMPLEX*16 array, dimension (N)


          The non-negative real scalars beta that define the


          eigenvalues of GNEP.  BETA(j) = T(j,j), the diagonal element


          of the triangular factor T.


          Together, the quantities alpha = ALPHA(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.

VSL

          VSL is COMPLEX*16 array, dimension (LDVSL,N)


          If JOBVSL = 'V', the matrix of left Schur vectors Q.


          Not referenced if JOBVSL = 'N'.

LDVSL

          LDVSL is INTEGER


          The leading dimension of the matrix VSL. LDVSL >= 1, and


          if JOBVSL = 'V', LDVSL >= N.

VSR

          VSR is COMPLEX*16 array, dimension (LDVSR,N)


          If JOBVSR = 'V', the matrix of right Schur vectors Z.


          Not referenced if JOBVSR = 'N'.

LDVSR

          LDVSR is INTEGER


          The leading dimension of the matrix VSR. LDVSR >= 1, and


          if JOBVSR = 'V', LDVSR >= N.

WORK

          WORK is COMPLEX*16 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(1,2*N).


          For good performance, LWORK must generally be larger.


          To compute the optimal value of LWORK, call ILAENV to get


          blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.)  Then compute:


          NB  -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR;


          the optimal LWORK is N*(NB+1).


          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.

RWORK

          RWORK is DOUBLE PRECISION array, dimension (3*N)

INFO

          INFO is INTEGER


          = 0:  successful exit


          < 0:  if INFO = -i, the i-th argument had an illegal value.


          =1,...,N:


                The QZ iteration failed.  (A,B) are not in Schur


                form, but ALPHA(j) and BETA(j) should be correct for


                j=INFO+1,...,N.


          > N:  errors that usually indicate LAPACK problems:


                =N+1: error return from ZGGBAL


                =N+2: error return from ZGEQRF


                =N+3: error return from ZUNMQR


                =N+4: error return from ZUNGQR


                =N+5: error return from ZGGHRD


                =N+6: error return from ZHGEQZ (other than failed


                                               iteration)


                =N+7: error return from ZGGBAK (computing VSL)


                =N+8: error return from ZGGBAK (computing VSR)


                =N+9: error return from ZLASCL (various places)

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2011