DHSEQR man page on IRIX

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DHSEQR(3F)							    DHSEQR(3F)

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-triangular 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-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
	     orthogonal 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 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.

									Page 1

DHSEQR(3F)							    DHSEQR(3F)

     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
	     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) 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 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 DORGHR after the call to DGEHRD
	     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) DOUBLE PRECISION 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, 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.

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