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 This routine is deprecated and has been replaced by routine DGGES.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