SRC/DEPRECATED/dgegs.f(3)

NAME
SRC/DEPRECATED/dgegs.f

SYNOPSIS

  Functions/Subroutines
subroutine dgegs (jobvsl, jobvsr, n, a, lda, b, ldb, alphar, alphai, beta, vsl, ldvsl, vsr, ldvsr, work, lwork, info)
DGEGS computes the eigenvalues, real Schur form, and, optionally, the left and/or right Schur vectors of a real matrix pair (A,B)

Function/Subroutine Documentation

  subroutine dgegs (character jobvsl, character jobvsr, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) alphar, double precision, dimension( * ) alphai, double precision, dimension( * ) beta, double precision, dimension( ldvsl, * ) vsl, integer ldvsl, double precision, dimension( ldvsr, * ) vsr, integer ldvsr, double precision, dimension( * ) work, integer lwork, integer info)

DGEGS computes the eigenvalues, real Schur form, and, optionally, the left and/or right Schur vectors of a real matrix pair (A,B)

Purpose:

     This routine is deprecated and has been replaced by routine DGGES.
     DGEGS computes the eigenvalues, real Schur form, and, optionally,
     left and or/right Schur vectors of a real matrix pair (A,B).
     Given two square matrices A and B, the generalized real Schur
     factorization has the form
       A = Q*S*Z**T,  B = Q*T*Z**T
     where Q and Z are orthogonal matrices, T is upper triangular, and S
     is an upper quasi-triangular matrix with 1-by-1 and 2-by-2 diagonal
     blocks, the 2-by-2 blocks corresponding to complex conjugate pairs
     of eigenvalues of (A,B).  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
     DGEGV should be used instead.  See DGEGV for a description of the
     eigenvalues of the generalized nonsymmetric eigenvalue problem
     (GNEP).

Parameters
    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 DOUBLE PRECISION array, dimension (LDA, N)
              On entry, the matrix A.
              On exit, the upper quasi-triangular matrix S from the
              generalized real Schur factorization.

    LDA

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

    B

              B is DOUBLE PRECISION array, dimension (LDB, N)
              On entry, the matrix B.
              On exit, the upper triangular matrix T from the generalized
              real Schur factorization.

    LDB

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

    ALPHAR

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

    ALPHAI

              ALPHAI is DOUBLE PRECISION 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 DOUBLE PRECISION 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.

    VSL

              VSL is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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(1,4*N).
              For good performance, LWORK must generally be larger.
              To compute the optimal value of LWORK, call ILAENV to get
              blocksizes (for DGEQRF, DORMQR, and DORGQR.)  Then compute:
              NB  -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR
              The optimal LWORK is  2*N + 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.

    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 ALPHAR(j), ALPHAI(j), and BETA(j) should
                    be correct for j=INFO+1,...,N.
              > N:  errors that usually indicate LAPACK problems:
                    =N+1: error return from DGGBAL
                    =N+2: error return from DGEQRF
                    =N+3: error return from DORMQR
                    =N+4: error return from DORGQR
                    =N+5: error return from DGGHRD
                    =N+6: error return from DHGEQZ (other than failed
                                                    iteration)
                    =N+7: error return from DGGBAK (computing VSL)
                    =N+8: error return from DGGBAK (computing VSR)
                    =N+9: error return from DLASCL (various places)

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 224 of file dgegs.f.

Author

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