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

DHSEQR(l)					)					DHSEQR(l)

NAME
       DHSEQR  - 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-tri-
       angular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors

SYNOPSIS
       SUBROUTINE DHSEQR( 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

	   DOUBLE	  PRECISION H( LDH, * ), WI( * ), WORK( * ), WR( * ), Z( LDZ, * )

PURPOSE
       DHSEQR  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-tri-
       angular matrix (the Schur form), and Z is the orthogonal matrix of Schur vectors.  Option-
       ally 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 orthogonal matrix Q on entry, and the prod-
	       uct 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 DGEBAL, and then passed to SGEHRD when the matrix output by DGEBAL  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) DOUBLE PRECISION 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 decomposition (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) DOUBLE PRECISION array, dimension (N)
	       WI      (output) DOUBLE PRECISION array, dimension  (N)	The  real  and	imaginary
	       parts,  respectively, of the computed eigenvalues. If two eigenvalues 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 eigen-
	       values 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) DOUBLE PRECISION 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  orthogo-
	       nal  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 orthogo-
	       nal matrix generated by DORGHR after the call to DGEHRD which formed  the  Hessen-
	       berg 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) DOUBLE PRECISION 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, DHSEQR 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.

LAPACK version 3.0			   15 June 2000 				DHSEQR(l)


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