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CHSEQR(l)			       )			     CHSEQR(l)

NAME
       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

SYNOPSIS
       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, * )

PURPOSE
       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 postmulti‐
       plied 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 Hessen‐
       berg 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  uni‐
	       tary 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  Hes‐
	       senberg	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 subma‐
	       trix 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  success‐
	       fully computed.

LAPACK version 3.0		 15 June 2000			     CHSEQR(l)
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