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dgegs.f(3)				      LAPACK				       dgegs.f(3)

NAME
       dgegs.f -

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

Function/Subroutine Documentation
   subroutine dgegs (characterJOBVSL, characterJOBVSR, integerN, double precision, dimension(
       lda, * )A, integerLDA, double precision, dimension( ldb, * )B, integerLDB, double
       precision, dimension( * )ALPHAR, double precision, dimension( * )ALPHAI, double precision,
       dimension( * )BETA, double precision, dimension( ldvsl, * )VSL, integerLDVSL, double
       precision, dimension( ldvsr, * )VSR, integerLDVSR, double precision, dimension( * )WORK,
       integerLWORK, integerINFO)
	DGEEVX 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	    This routine is deprecated and has been replaced by routine DGGES.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.

       Date:
	   November 2011

       Definition at line 226 of file dgegs.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			       dgegs.f(3)
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