SRC/DEPRECATED/sgegs.f(3)

NAME
SRC/DEPRECATED/sgegs.f

SYNOPSIS

  Functions/Subroutines
subroutine sgegs (jobvsl, jobvsr, n, a, lda, b, ldb, alphar, alphai, beta, vsl, ldvsl, vsr, ldvsr, work, lwork, info)
SGEGS 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 sgegs (character jobvsl, character jobvsr, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) alphar, real, dimension( * ) alphai, real, dimension( * ) beta, real, dimension( ldvsl, * ) vsl, integer ldvsl, real, dimension( ldvsr, * ) vsr, integer ldvsr, real, dimension( * ) work, integer lwork, integer info)

SGEGS 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 This routine is deprecated and has been replaced by routine SGGES.
    !>
    !> SGEGS 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
    !> SGEGV should be used instead.  See SGEGV 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 REAL 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 REAL 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 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.
    !>

    VSL

    !>          VSL is REAL 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 REAL 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 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(1,4*N).
    !>          For good performance, LWORK must generally be larger.
    !>          To compute the optimal value of LWORK, call ILAENV to get
    !>          blocksizes (for SGEQRF, SORMQR, and SORGQR.)  Then compute:
    !>          NB  -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR
    !>          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 SGGBAL
    !>                =N+2: error return from SGEQRF
    !>                =N+3: error return from SORMQR
    !>                =N+4: error return from SORGQR
    !>                =N+5: error return from SGGHRD
    !>                =N+6: error return from SHGEQZ (other than failed
    !>                                                iteration)
    !>                =N+7: error return from SGGBAK (computing VSL)
    !>                =N+8: error return from SGGBAK (computing VSR)
    !>                =N+9: error return from SLASCL (various places)
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 224 of file sgegs.f.

Author

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