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slahqr.f(3)				      LAPACK				      slahqr.f(3)

NAME
       slahqr.f -

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

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

       Purpose:

	       SLAHQR is an auxiliary routine called by SHSEQR to update the
	       eigenvalues and Schur decomposition already computed by SHSEQR, 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 quasi-triangular in
		     rows and columns IHI+1:N, and that H(ILO,ILO-1) = 0 (unless
		     ILO = 1). SLAHQR 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 REAL array, dimension (LDH,N)
		     On entry, the upper Hessenberg matrix H.
		     On exit, if INFO is zero and if WANTT is .TRUE., H is upper
		     quasi-triangular in rows and columns ILO:IHI, with any
		     2-by-2 diagonal blocks in standard form. If INFO is zero
		     and WANTT is .FALSE., the contents of H are unspecified on
		     exit.  The output state of H if INFO is nonzero is given
		     below under the description of INFO.

	   LDH

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

	   WR

		     WR is REAL array, dimension (N)

	   WI

		     WI is REAL array, dimension (N)
		     The real and imaginary parts, respectively, of the computed
		     eigenvalues ILO to IHI are stored in the corresponding
		     elements of WR and WI. 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 WANTT is .TRUE., 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).

	   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 REAL array, dimension (LDZ,N)
		     If WANTZ is .TRUE., on entry Z must contain the current
		     matrix Z of transformations accumulated by SHSEQR, 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, SLAHQR failed to compute all the
			     eigenvalues ILO to IHI in a total of 30 iterations
			     per eigenvalue; elements i+1:ihi of WR and WI
			     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

       Further Details:

		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 SLAHQR 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 207 of file slahqr.f.

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

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