CXML
        	    
LAPACK version 3.0
chseqr(3)

PURPOSE
  CHSEQR - compute the eigenvalues of a complex upper Hessenberg matrix H,
  and, optionally, the matrices T and Z from the Schur decomposition H = Z T
  Z**H, where T is an upper triangular matrix (the Schur form), and Z is the
  unitary matrix of Schur vectors

SYNTAX
  SUBROUTINE CHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, W, Z, LDZ, WORK, LWORK,
		     INFO )

      CHARACTER	     COMPZ, JOB

      INTEGER	     IHI, ILO, INFO, LDH, LDZ, LWORK, N

      COMPLEX	     H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )

DESCRIPTION
  CHSEQR computes the eigenvalues of a complex upper Hessenberg matrix H,
  and, optionally, the matrices T and Z from the Schur decomposition H = Z T
  Z**H, where T is an upper triangular matrix (the Schur form), and Z is the
  unitary matrix of Schur vectors.  Optionally Z may be postmultiplied into
  an input unitary matrix Q, so that this routine can give the Schur
  factorization of a matrix A which has been reduced to the Hessenberg form H
  by the unitary matrix Q:  A = Q*H*Q**H = (QZ)*T*(QZ)**H.

ARGUMENTS
  JOB	  (input) CHARACTER*1
	  = 'E': compute eigenvalues only;
	  = 'S': compute eigenvalues and the Schur form T.

  COMPZ	  (input) CHARACTER*1
	  = 'N': no Schur vectors are computed;
	  = 'I': Z is initialized to the unit matrix and the matrix Z of
	  Schur vectors of H is returned; = 'V': Z must contain an unitary
	  matrix Q on entry, and the product Q*Z is returned.

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

  ILO	  (input) INTEGER
	  IHI	  (input) INTEGER It is assumed that H is already upper
	  triangular in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are
	  normally set by a previous call to CGEBAL, and then passed to
	  CGEHRD when the matrix output by CGEBAL is reduced to Hessenberg
	  form. Otherwise ILO and IHI should be set to 1 and N respectively.
	  1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.

  H	  (input/output) COMPLEX array, dimension (LDH,N)
	  On entry, the upper Hessenberg matrix H.  On exit, if JOB = 'S', H
	  contains the upper triangular matrix T from the Schur decomposition
	  (the Schur form). If JOB = 'E', the contents of H are unspecified
	  on exit.

  LDH	  (input) INTEGER
	  The leading dimension of the array H. LDH >= max(1,N).

  W	  (output) COMPLEX array, dimension (N)
	  The computed eigenvalues. If JOB = 'S', the eigenvalues are stored
	  in the same order as on the diagonal of the Schur form returned in
	  H, with W(i) = H(i,i).

  Z	  (input/output) COMPLEX array, dimension (LDZ,N)
	  If COMPZ = 'N': Z is not referenced.
	  If COMPZ = 'I': on entry, Z need not be set, and on exit, Z
	  contains the unitary matrix Z of the Schur vectors of H.  If COMPZ
	  = 'V': on entry Z must contain an N-by-N matrix Q, which is assumed
	  to be equal to the unit matrix except for the submatrix
	  Z(ILO:IHI,ILO:IHI); on exit Z contains Q*Z.  Normally Q is the
	  unitary matrix generated by CUNGHR after the call to CGEHRD which
	  formed the Hessenberg matrix H.

  LDZ	  (input) INTEGER
	  The leading dimension of the array Z.	 LDZ >= max(1,N) if COMPZ =
	  'I' or 'V'; LDZ >= 1 otherwise.

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

  LWORK	  (input) INTEGER
	  The dimension of the array WORK.  LWORK >= max(1,N).

	  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	  (output) INTEGER
	  = 0:	successful exit
	  < 0:	if INFO = -i, the i-th argument had an illegal value
	  > 0:	if INFO = i, CHSEQR failed to compute all the eigenvalues in
	  a total of 30*(IHI-ILO+1) iterations; elements 1:ilo-1 and i+1:n of
	  W contain those eigenvalues which have been successfully computed.