SHSEQR(l)		LAPACK routine (version	1.1)		    SHSEQR(l)

NAME
  SHSEQR - compute the eigenvalues of a	real upper Hessenberg matrix H and,
  optionally, the matrices T and Z from	the Schur decomposition	H = Z T	Z**T,
  where	T is an	upper quasi-triangular matrix (the Schur form),	and Z is the
  orthogonal matrix of Schur vectors

SYNOPSIS

  SUBROUTINE SHSEQR( JOB, COMPZ, N, ILO, IHI, H, LDH, WR, WI, Z, LDZ, WORK,
		     LWORK, INFO )

      CHARACTER	     COMPZ, JOB

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

      REAL	     H(	LDH, * ), WI( *	), WORK( * ), WR( * ), Z( LDZ, * )

PURPOSE
  SHSEQR computes the eigenvalues of a real upper Hessenberg matrix H and,
  optionally, the matrices T and Z from	the Schur decomposition	H = Z T	Z**T,
  where	T is an	upper quasi-triangular matrix (the Schur form),	and Z is the
  orthogonal matrix of Schur vectors.

  Optionally Z may be postmultiplied into an input orthogonal 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 orthogonal matrix Q:  A =
  Q*H*Q**T = (QZ)*T*(QZ)**T.

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 orthogo-
	  nal 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	tri-
	  angular in rows and columns 1:ILO-1 and IHI+1:N. ILO and IHI are
	  normally set by a previous call to SGEBAL, and then passed to
	  SGEHRD when the matrix output	by SGEBAL is reduced to	Hessenberg
	  form.	Otherwise ILO and IHI should be	set to 1 and N respectively.
	  1 <= ILO <= max(1,IHI); IHI <= N.

  H	  (input/output) REAL array, dimension (LDH,N)
	  On entry, the	upper Hessenberg matrix	H.  On exit, if	JOB = 'S', H
	  contains the upper quasi-triangular matrix T from the	Schur decom-
	  position (the	Schur form); 2-by-2 diagonal blocks (corresponding to
	  complex conjugate pairs of eigenvalues) are returned in standard
	  form,	with H(i,i) = H(i+1,i+1) and H(i+1,i)*H(i,i+1) < 0. 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).

  WR	  (output) REAL	array, dimension (N)
	  WI	  (output) REAL	array, dimension (N) The real and imaginary
	  parts, respectively, of the computed eigenvalues. If two eigen-
	  values are computed as a complex conjugate pair, they	are stored in
	  consecutive elements of WR and WI, say the i-th and (i+1)th, with
	  WI(i)	> 0 and	WI(i+1)	< 0. If	JOB = 'S', the eigenvalues are stored
	  in the same order as on the diagonal of the Schur form returned in
	  H, with WR(i)	= H(i,i) and, if H(i:i+1,i:i+1)	is a 2-by-2 diagonal
	  block, WI(i) = sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(i).

  Z	  (input/output) REAL 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 con-
	  tains	the orthogonal 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
	  orthogonal matrix generated by SORGHR	after the call to SGEHRD
	  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) REAL array, dimension (N)

  LWORK	  (input) INTEGER
	  This argument	is currently redundant.

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