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sgees.f(3)				      LAPACK				       sgees.f(3)

       sgees.f -

       subroutine sgees (JOBVS, SORT, SELECT, N, A, LDA, SDIM, WR, WI, VS, LDVS, WORK, LWORK,
	    SGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur
	   vectors for GE matrices

Function/Subroutine Documentation
   subroutine sgees (characterJOBVS, characterSORT, logical, externalSELECT, integerN, real,
       dimension( lda, * )A, integerLDA, integerSDIM, real, dimension( * )WR, real, dimension( *
       )WI, real, dimension( ldvs, * )VS, integerLDVS, real, dimension( * )WORK, integerLWORK,
       logical, dimension( * )BWORK, integerINFO)
	SGEES computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur
       vectors for GE matrices


	    SGEES computes for an N-by-N real nonsymmetric matrix A, the
	    eigenvalues, the real Schur form T, and, optionally, the matrix of
	    Schur vectors Z.  This gives the Schur factorization A = Z*T*(Z**T).

	    Optionally, it also orders the eigenvalues on the diagonal of the
	    real Schur form so that selected eigenvalues are at the top left.
	    The leading columns of Z then form an orthonormal basis for the
	    invariant subspace corresponding to the selected eigenvalues.

	    A matrix is in real Schur form if it is upper quasi-triangular with
	    1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in the
		    [  a  b  ]
		    [  c  a  ]

	    where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).


		     = 'N': Schur vectors are not computed;
		     = 'V': Schur vectors are computed.


		     SORT is CHARACTER*1
		     Specifies whether or not to order the eigenvalues on the
		     diagonal of the Schur form.
		     = 'N': Eigenvalues are not ordered;
		     = 'S': Eigenvalues are ordered (see SELECT).


		     SELECT is LOGICAL FUNCTION of two REAL arguments
		     SELECT must be declared EXTERNAL in the calling subroutine.
		     If SORT = 'S', SELECT is used to select eigenvalues to sort
		     to the top left of the Schur form.
		     If SORT = 'N', SELECT is not referenced.
		     An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if
		     SELECT(WR(j),WI(j)) is true; i.e., if either one of a complex
		     conjugate pair of eigenvalues is selected, then both complex
		     eigenvalues are selected.
		     Note that a selected complex eigenvalue may no longer
		     satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since
		     ordering may change the value of complex eigenvalues
		     (especially if the eigenvalue is ill-conditioned); in this
		     case INFO is set to N+2 (see INFO below).


		     N is INTEGER
		     The order of the matrix A. N >= 0.


		     A is REAL array, dimension (LDA,N)
		     On entry, the N-by-N matrix A.
		     On exit, A has been overwritten by its real Schur form T.


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


		     SDIM is INTEGER
		     If SORT = 'N', SDIM = 0.
		     If SORT = 'S', SDIM = number of eigenvalues (after sorting)
				    for which SELECT is true. (Complex conjugate
				    pairs for which SELECT is true for either
				    eigenvalue count as 2.)


		     WR is REAL array, dimension (N)


		     WI is REAL array, dimension (N)
		     WR and WI contain the real and imaginary parts,
		     respectively, of the computed eigenvalues in the same order
		     that they appear on the diagonal of the output Schur form T.
		     Complex conjugate pairs of eigenvalues will appear
		     consecutively with the eigenvalue having the positive
		     imaginary part first.


		     VS is REAL array, dimension (LDVS,N)
		     If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur
		     If JOBVS = 'N', VS is not referenced.


		     LDVS is INTEGER
		     The leading dimension of the array VS.  LDVS >= 1; if
		     JOBVS = 'V', LDVS >= N.


		     WORK is REAL array, dimension (MAX(1,LWORK))
		     On exit, if INFO = 0, WORK(1) contains the optimal LWORK.


		     The dimension of the array WORK.  LWORK >= max(1,3*N).
		     For good performance, LWORK must generally be larger.

		     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.


		     BWORK is LOGICAL array, dimension (N)
		     Not referenced if SORT = 'N'.


		     INFO is INTEGER
		     = 0: successful exit
		     < 0: if INFO = -i, the i-th argument had an illegal value.
		     > 0: if INFO = i, and i is
			<= N: the QR algorithm failed to compute all the
			      eigenvalues; elements 1:ILO-1 and i+1:N of WR and WI
			      contain those eigenvalues which have converged; if
			      JOBVS = 'V', VS contains the matrix which reduces A
			      to its partially converged Schur form.
			= N+1: the eigenvalues could not be reordered because some
			      eigenvalues were too close to separate (the problem
			      is very ill-conditioned);
			= N+2: after reordering, roundoff changed values of some
			      complex eigenvalues so that leading eigenvalues in
			      the Schur form no longer satisfy SELECT=.TRUE.  This
			      could also be caused by underflow due to scaling.

	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

	   November 2011

       Definition at line 216 of file sgees.f.

       Generated automatically by Doxygen for LAPACK from the source code.

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