zlahqr.f(3)							      LAPACK							       zlahqr.f(3)

NAME

       zlahqr.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zlahqr (WANTT, WANTZ, N, ILO, IHI, H, LDH, W, ILOZ, IHIZ, Z, LDZ, INFO)
	   ZLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR
	   algorithm.

Function/Subroutine Documentation
   subroutine zlahqr (logicalWANTT, logicalWANTZ, integerN, integerILO, integerIHI, complex*16, dimension( ldh, * )H, integerLDH, complex*16,
       dimension( * )W, integerILOZ, integerIHIZ, complex*16, dimension( ldz, * )Z, integerLDZ, integerINFO)
       ZLAHQR computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, using the double-shift/single-shift QR algorithm.

       Purpose:

	       ZLAHQR is an auxiliary routine called by CHSEQR to update the
	       eigenvalues and Schur decomposition already computed by CHSEQR, by
	       dealing with the Hessenberg submatrix in rows and columns ILO to
	       IHI.

       Parameters:
	   WANTT

		     WANTT is LOGICAL
		     = .TRUE. : the full Schur form T is required;
		     = .FALSE.: only eigenvalues are required.

	   WANTZ

		     WANTZ is LOGICAL
		     = .TRUE. : the matrix of Schur vectors Z is required;
		     = .FALSE.: Schur vectors are not required.

	   N

		     N is INTEGER
		     The order of the matrix H.  N >= 0.

	   ILO

		     ILO is INTEGER

	   IHI

		     IHI is INTEGER
		     It is assumed that H is already upper triangular in rows and
		     columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless ILO = 1).
		     ZLAHQR works primarily with the Hessenberg submatrix in rows
		     and columns ILO to IHI, but applies transformations to all of
		     H if WANTT is .TRUE..
		     1 <= ILO <= max(1,IHI); IHI <= N.

	   H

		     H is COMPLEX*16 array, dimension (LDH,N)
		     On entry, the upper Hessenberg matrix H.
		     On exit, if INFO is zero and if WANTT is .TRUE., then H
		     is upper triangular in rows and columns ILO:IHI.  If INFO
		     is zero and if WANTT is .FALSE., then the contents of H
		     are unspecified on exit.  The output state of H in case
		     INF is positive is below under the description of INFO.

	   LDH

		     LDH is INTEGER
		     The leading dimension of the array H. LDH >= max(1,N).

	   W

		     W is COMPLEX*16 array, dimension (N)
		     The computed eigenvalues ILO to IHI are stored in the
		     corresponding elements of W. If WANTT is .TRUE., 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).

	   ILOZ

		     ILOZ is INTEGER

	   IHIZ

		     IHIZ is INTEGER
		     Specify the rows of Z to which transformations must be
		     applied if WANTZ is .TRUE..
		     1 <= ILOZ <= ILO; IHI <= IHIZ <= N.

	   Z

		     Z is COMPLEX*16 array, dimension (LDZ,N)
		     If WANTZ is .TRUE., on entry Z must contain the current
		     matrix Z of transformations accumulated by CHSEQR, and on
		     exit Z has been updated; transformations are applied only to
		     the submatrix Z(ILOZ:IHIZ,ILO:IHI).
		     If WANTZ is .FALSE., Z is not referenced.

	   LDZ

		     LDZ is INTEGER
		     The leading dimension of the array Z. LDZ >= max(1,N).

	   INFO

		     INFO is INTEGER
		      =   0: successful exit
		     .GT. 0: if INFO = i, ZLAHQR failed to compute all the
			     eigenvalues ILO to IHI in a total of 30 iterations
			     per eigenvalue; elements i+1:ihi of W contain
			     those eigenvalues which have been successfully
			     computed.

			     If INFO .GT. 0 and WANTT is .FALSE., then on exit,
			     the remaining unconverged eigenvalues are the
			     eigenvalues of the upper Hessenberg matrix
			     rows and columns ILO thorugh INFO of the final,
			     output value of H.

			     If INFO .GT. 0 and WANTT is .TRUE., then on exit
		     (*)       (initial value of H)*U  = U*(final value of H)
			     where U is an orthognal matrix.	The final
			     value of H is upper Hessenberg and triangular in
			     rows and columns INFO+1 through IHI.

			     If INFO .GT. 0 and WANTZ is .TRUE., then on exit
				 (final value of Z)  = (initial value of Z)*U
			     where U is the orthogonal matrix in (*)
			     (regardless of the value of WANTT.)

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:

		02-96 Based on modifications by
		David Day, Sandia National Laboratory, USA

		12-04 Further modifications by
		Ralph Byers, University of Kansas, USA
		This is a modified version of ZLAHQR from LAPACK version 3.0.
		It is (1) more robust against overflow and underflow and
		(2) adopts the more conservative Ahues & Tisseur stopping
		criterion (LAWN 122, 1997).

       Definition at line 195 of file zlahqr.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       zlahqr.f(3)