sgegs.f(3)

NAME
sgegs.f -

SYNOPSIS

  Functions/Subroutines
subroutine SGEGS (JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LWORK, INFO)
SGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation

  subroutine SGEGS (CHARACTERJOBVSL, CHARACTERJOBVSR, INTEGERN, REAL, dimension( lda, * )A, INTEGERLDA, REAL, dimension( ldb, * )B, INTEGERLDB, REAL, dimension( * )ALPHAR, REAL, dimension( * )ALPHAI, REAL, dimension( * )BETA, REAL, dimension( ldvsl, * )VSL, INTEGERLDVSL, REAL, dimension( ldvsr, * )VSR, INTEGERLDVSR, REAL, dimension( * )WORK, INTEGERLWORK, INTEGERINFO)

SGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

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     This routine is deprecated and has been replaced by routine SGGES.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'.

Date:
    November 2011

Definition at line 226 of file sgegs.f'.

Author

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