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RedHat 9 (Linux i386) - man page for zhseqr (redhat section l)

ZHSEQR(l)					)					ZHSEQR(l)

NAME
       ZHSEQR  - 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 trian-
       gular matrix (the Schur form), and Z is the unitary matrix of Schur vectors

SYNOPSIS
       SUBROUTINE ZHSEQR( 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*16	  H( LDH, * ), W( * ), WORK( * ), Z( LDZ, * )

PURPOSE
       ZHSEQR  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 trian-
       gular 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 ZGEBAL, and then passed to CGEHRD when the matrix output by ZGEBAL  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*16 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*16 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*16 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 sub-
	       matrix Z(ILO:IHI,ILO:IHI); on exit Z contains Q*Z.   Normally  Q  is  the  unitary
	       matrix  generated  by  ZUNGHR after the call to ZGEHRD 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*16 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, ZHSEQR 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 eigenval-
	       ues which have been successfully computed.

LAPACK version 3.0			   15 June 2000 				ZHSEQR(l)


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