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cgees(3P)		    Sun Performance Library		     cgees(3P)

NAME
       cgees - compute for an N-by-N complex nonsymmetric matrix A, the eigen‐
       values, the Schur form T, and, optionally, the matrix of Schur  vectors
       Z

SYNOPSIS
       SUBROUTINE CGEES(JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, W, Z, LDZ,
	     WORK, LDWORK, WORK2, WORK3, INFO)

       CHARACTER * 1 JOBZ, SORTEV
       COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
       INTEGER N, LDA, NOUT, LDZ, LDWORK, INFO
       LOGICAL SELECT
       LOGICAL WORK3(*)
       REAL WORK2(*)

       SUBROUTINE CGEES_64(JOBZ, SORTEV, SELECT, N, A, LDA, NOUT, W, Z, LDZ,
	     WORK, LDWORK, WORK2, WORK3, INFO)

       CHARACTER * 1 JOBZ, SORTEV
       COMPLEX A(LDA,*), W(*), Z(LDZ,*), WORK(*)
       INTEGER*8 N, LDA, NOUT, LDZ, LDWORK, INFO
       LOGICAL*8 SELECT
       LOGICAL*8 WORK3(*)
       REAL WORK2(*)

   F95 INTERFACE
       SUBROUTINE GEES(JOBZ, SORTEV, SELECT, [N], A, [LDA], [NOUT], W, Z, [LDZ],
	      [WORK], [LDWORK], [WORK2], [WORK3], [INFO])

       CHARACTER(LEN=1) :: JOBZ, SORTEV
       COMPLEX, DIMENSION(:) :: W, WORK
       COMPLEX, DIMENSION(:,:) :: A, Z
       INTEGER :: N, LDA, NOUT, LDZ, LDWORK, INFO
       LOGICAL :: SELECT
       LOGICAL, DIMENSION(:) :: WORK3
       REAL, DIMENSION(:) :: WORK2

       SUBROUTINE GEES_64(JOBZ, SORTEV, SELECT, [N], A, [LDA], [NOUT], W, Z,
	      [LDZ], [WORK], [LDWORK], [WORK2], [WORK3], [INFO])

       CHARACTER(LEN=1) :: JOBZ, SORTEV
       COMPLEX, DIMENSION(:) :: W, WORK
       COMPLEX, DIMENSION(:,:) :: A, Z
       INTEGER(8) :: N, LDA, NOUT, LDZ, LDWORK, INFO
       LOGICAL(8) :: SELECT
       LOGICAL(8), DIMENSION(:) :: WORK3
       REAL, DIMENSION(:) :: WORK2

   C INTERFACE
       #include <sunperf.h>

       void  cgees(char	 jobz, char sortev, int(*select)(complex), int n, com‐
		 plex *a, int lda, int *nout, complex *w, complex *z, int ldz,
		 int *info);

       void  cgees_64(char  jobz, char sortev, long(*select)(complex), long n,
		 complex *a, long lda, long *nout,  complex  *w,  complex  *z,
		 long ldz, long *info);

PURPOSE
       cgees  computes for an N-by-N complex nonsymmetric matrix A, the eigen‐
       values, the Schur form T, and, optionally, the matrix of Schur  vectors
       Z.  This gives the Schur factorization A = Z*T*(Z**H).

       Optionally, it also orders the eigenvalues on the diagonal of the 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 complex matrix is in Schur form if it is upper triangular.

ARGUMENTS
       JOBZ (input)
		 = 'N': Schur vectors are not computed;
		 = 'V': Schur vectors are computed.

       SORTEV (input)
		 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 (input)
		 LOGICAL FUNCTION of  one  COMPLEX  argument  SELECT  must  be
		 declared  EXTERNAL  in	 the  calling subroutine.  If SORTEV =
		 'S', SELECT is used to select eigenvalues to order to the top
		 left  of the Schur form.  If SORTEV = 'N', SELECT is not ref‐
		 erenced.  The eigenvalue W(j) is selected if SELECT(W(j))  is
		 true.

       N (input) The order of the matrix A. N >= 0.

       A (input/output)
		 COMPLEX  array,  dimension(LDA,N) On entry, the N-by-N matrix
		 A.  On exit, A has been overwritten by its Schur form T.

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

       NOUT (output)
		 If SORTEV = 'N', NOUT = 0.  If SORTEV = 'S', NOUT = number of
		 eigenvalues for which SELECT is true.

       W (output)
		 COMPLEX array, dimension(N) W contains the computed eigenval‐
		 ues, in the same order that they appear on  the  diagonal  of
		 the output Schur form T.

       Z (output)
		 COMPLEX array, dimension(LDZ,N) If JOBZ = 'V', Z contains the
		 unitary matrix Z of Schur vectors.  If JOBZ = 'N', Z  is  not
		 referenced.

       LDZ (input)
		 The  leading  dimension  of the array Z.  LDZ >= 1; if JOBZ =
		 'V', LDZ >= N.

       WORK (workspace)
		 COMPLEX array, dimension(LWORK) On exit, if INFO = 0, WORK(1)
		 returns the optimal LDWORK.

       LDWORK (input)
		 The  dimension of the array WORK.  LDWORK >= max(1,2*N).  For
		 good performance, LDWORK must generally be larger.

		 If LDWORK = -1, then a workspace query is assumed;  the  rou‐
		 tine  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 LDWORK is issued by XERBLA.

       WORK2 (workspace)
		 REAL array, dimension(N)

       WORK3 (workspace)
		 LOGICAL array, dimension(N) Not referenced if SORTEV = 'N'.

       INFO (output)
		 = 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 W contain those
		 eigenvalues which have converged; if JOBZ = 'V',  Z  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 scal‐
		 ing.

				  6 Mar 2009			     cgees(3P)
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