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dlaqr3.f(3)				      LAPACK				      dlaqr3.f(3)

NAME
       dlaqr3.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlaqr3 (WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND,
	   SR, SI, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK)
	   DLAQR3 performs the orthogonal similarity transformation of a Hessenberg matrix to
	   detect and deflate fully converged eigenvalues from a trailing principal submatrix
	   (aggressive early deflation).

Function/Subroutine Documentation
   subroutine dlaqr3 (logicalWANTT, logicalWANTZ, integerN, integerKTOP, integerKBOT, integerNW,
       double precision, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, double
       precision, dimension( ldz, * )Z, integerLDZ, integerNS, integerND, double precision,
       dimension( * )SR, double precision, dimension( * )SI, double precision, dimension( ldv, *
       )V, integerLDV, integerNH, double precision, dimension( ldt, * )T, integerLDT, integerNV,
       double precision, dimension( ldwv, * )WV, integerLDWV, double precision, dimension( *
       )WORK, integerLWORK)
       DLAQR3 performs the orthogonal similarity transformation of a Hessenberg matrix to detect
       and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive
       early deflation).

       Purpose:

	       Aggressive early deflation:

	       DLAQR3 accepts as input an upper Hessenberg matrix
	       H and performs an orthogonal similarity transformation
	       designed to detect and deflate fully converged eigenvalues from
	       a trailing principal submatrix.	On output H has been over-
	       written by a new Hessenberg matrix that is a perturbation of
	       an orthogonal similarity transformation of H.  It is to be
	       hoped that the final version of H has many zero subdiagonal
	       entries.

       Parameters:
	   WANTT

		     WANTT is LOGICAL
		     If .TRUE., then the Hessenberg matrix H is fully updated
		     so that the quasi-triangular Schur factor may be
		     computed (in cooperation with the calling subroutine).
		     If .FALSE., then only enough of H is updated to preserve
		     the eigenvalues.

	   WANTZ

		     WANTZ is LOGICAL
		     If .TRUE., then the orthogonal matrix Z is updated so
		     so that the orthogonal Schur factor may be computed
		     (in cooperation with the calling subroutine).
		     If .FALSE., then Z is not referenced.

	   N

		     N is INTEGER
		     The order of the matrix H and (if WANTZ is .TRUE.) the
		     order of the orthogonal matrix Z.

	   KTOP

		     KTOP is INTEGER
		     It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0.
		     KBOT and KTOP together determine an isolated block
		     along the diagonal of the Hessenberg matrix.

	   KBOT

		     KBOT is INTEGER
		     It is assumed without a check that either
		     KBOT = N or H(KBOT+1,KBOT)=0.  KBOT and KTOP together
		     determine an isolated block along the diagonal of the
		     Hessenberg matrix.

	   NW

		     NW is INTEGER
		     Deflation window size.  1 .LE. NW .LE. (KBOT-KTOP+1).

	   H

		     H is DOUBLE PRECISION array, dimension (LDH,N)
		     On input the initial N-by-N section of H stores the
		     Hessenberg matrix undergoing aggressive early deflation.
		     On output H has been transformed by an orthogonal
		     similarity transformation, perturbed, and the returned
		     to Hessenberg form that (it is to be hoped) has some
		     zero subdiagonal entries.

	   LDH

		     LDH is integer
		     Leading dimension of H just as declared in the calling
		     subroutine.  N .LE. LDH

	   ILOZ

		     ILOZ is INTEGER

	   IHIZ

		     IHIZ is INTEGER
		     Specify the rows of Z to which transformations must be
		     applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N.

	   Z

		     Z is DOUBLE PRECISION array, dimension (LDZ,N)
		     IF WANTZ is .TRUE., then on output, the orthogonal
		     similarity transformation mentioned above has been
		     accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right.
		     If WANTZ is .FALSE., then Z is unreferenced.

	   LDZ

		     LDZ is integer
		     The leading dimension of Z just as declared in the
		     calling subroutine.  1 .LE. LDZ.

	   NS

		     NS is integer
		     The number of unconverged (ie approximate) eigenvalues
		     returned in SR and SI that may be used as shifts by the
		     calling subroutine.

	   ND

		     ND is integer
		     The number of converged eigenvalues uncovered by this
		     subroutine.

	   SR

		     SR is DOUBLE PRECISION array, dimension (KBOT)

	   SI

		     SI is DOUBLE PRECISION array, dimension (KBOT)
		     On output, the real and imaginary parts of approximate
		     eigenvalues that may be used for shifts are stored in
		     SR(KBOT-ND-NS+1) through SR(KBOT-ND) and
		     SI(KBOT-ND-NS+1) through SI(KBOT-ND), respectively.
		     The real and imaginary parts of converged eigenvalues
		     are stored in SR(KBOT-ND+1) through SR(KBOT) and
		     SI(KBOT-ND+1) through SI(KBOT), respectively.

	   V

		     V is DOUBLE PRECISION array, dimension (LDV,NW)
		     An NW-by-NW work array.

	   LDV

		     LDV is integer scalar
		     The leading dimension of V just as declared in the
		     calling subroutine.  NW .LE. LDV

	   NH

		     NH is integer scalar
		     The number of columns of T.  NH.GE.NW.

	   T

		     T is DOUBLE PRECISION array, dimension (LDT,NW)

	   LDT

		     LDT is integer
		     The leading dimension of T just as declared in the
		     calling subroutine.  NW .LE. LDT

	   NV

		     NV is integer
		     The number of rows of work array WV available for
		     workspace.  NV.GE.NW.

	   WV

		     WV is DOUBLE PRECISION array, dimension (LDWV,NW)

	   LDWV

		     LDWV is integer
		     The leading dimension of W just as declared in the
		     calling subroutine.  NW .LE. LDV

	   WORK

		     WORK is DOUBLE PRECISION array, dimension (LWORK)
		     On exit, WORK(1) is set to an estimate of the optimal value
		     of LWORK for the given values of N, NW, KTOP and KBOT.

	   LWORK

		     LWORK is integer
		     The dimension of the work array WORK.  LWORK = 2*NW
		     suffices, but greater efficiency may result from larger
		     values of LWORK.

		     If LWORK = -1, then a workspace query is assumed; DLAQR3
		     only estimates the optimal workspace size for the given
		     values of N, NW, KTOP and KBOT.  The estimate is returned
		     in WORK(1).  No error message related to LWORK is issued
		     by XERBLA.  Neither H nor Z are accessed.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

       Contributors:
	   Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA

       Definition at line 274 of file dlaqr3.f.

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

Version 3.4.2				 Tue Sep 25 2012			      dlaqr3.f(3)
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