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CentOS 7.0 - man page for dlaqr5 (centos section 3)

dlaqr5.f(3)				      LAPACK				      dlaqr5.f(3)

NAME
       dlaqr5.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlaqr5 (WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, SR, SI, H, LDH, ILOZ,
	   IHIZ, Z, LDZ, V, LDV, U, LDU, NV, WV, LDWV, NH, WH, LDWH)
	   DLAQR5 performs a single small-bulge multi-shift QR sweep.

Function/Subroutine Documentation
   subroutine dlaqr5 (logicalWANTT, logicalWANTZ, integerKACC22, integerN, integerKTOP,
       integerKBOT, integerNSHFTS, double precision, dimension( * )SR, double precision,
       dimension( * )SI, double precision, dimension( ldh, * )H, integerLDH, integerILOZ,
       integerIHIZ, double precision, dimension( ldz, * )Z, integerLDZ, double precision,
       dimension( ldv, * )V, integerLDV, double precision, dimension( ldu, * )U, integerLDU,
       integerNV, double precision, dimension( ldwv, * )WV, integerLDWV, integerNH, double
       precision, dimension( ldwh, * )WH, integerLDWH)
       DLAQR5 performs a single small-bulge multi-shift QR sweep.

       Purpose:

	       DLAQR5, called by DLAQR0, performs a
	       single small-bulge multi-shift QR sweep.

       Parameters:
	   WANTT

		     WANTT is logical scalar
			WANTT = .true. if the quasi-triangular Schur factor
			is being computed.  WANTT is set to .false. otherwise.

	   WANTZ

		     WANTZ is logical scalar
			WANTZ = .true. if the orthogonal Schur factor is being
			computed.  WANTZ is set to .false. otherwise.

	   KACC22

		     KACC22 is integer with value 0, 1, or 2.
			Specifies the computation mode of far-from-diagonal
			orthogonal updates.
		   = 0: DLAQR5 does not accumulate reflections and does not
			use matrix-matrix multiply to update far-from-diagonal
			matrix entries.
		   = 1: DLAQR5 accumulates reflections and uses matrix-matrix
			multiply to update the far-from-diagonal matrix entries.
		   = 2: DLAQR5 accumulates reflections, uses matrix-matrix
			multiply to update the far-from-diagonal matrix entries,
			and takes advantage of 2-by-2 block structure during
			matrix multiplies.

	   N

		     N is integer scalar
			N is the order of the Hessenberg matrix H upon which this
			subroutine operates.

	   KTOP

		     KTOP is integer scalar

	   KBOT

		     KBOT is integer scalar
			These are the first and last rows and columns of an
			isolated diagonal block upon which the QR sweep is to be
			applied. It is assumed without a check that
				  either KTOP = 1  or	H(KTOP,KTOP-1) = 0
			and
				  either KBOT = N  or	H(KBOT+1,KBOT) = 0.

	   NSHFTS

		     NSHFTS is integer scalar
			NSHFTS gives the number of simultaneous shifts.  NSHFTS
			must be positive and even.

	   SR

		     SR is DOUBLE PRECISION array of size (NSHFTS)

	   SI

		     SI is DOUBLE PRECISION array of size (NSHFTS)
			SR contains the real parts and SI contains the imaginary
			parts of the NSHFTS shifts of origin that define the
			multi-shift QR sweep.  On output SR and SI may be
			reordered.

	   H

		     H is DOUBLE PRECISION array of size (LDH,N)
			On input H contains a Hessenberg matrix.  On output a
			multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied
			to the isolated diagonal block in rows and columns KTOP
			through KBOT.

	   LDH

		     LDH is integer scalar
			LDH is the leading dimension of H just as declared in the
			calling procedure.  LDH.GE.MAX(1,N).

	   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 of size (LDZ,IHI)
			If WANTZ = .TRUE., then the QR Sweep orthogonal
			similarity transformation is accumulated into
			Z(ILOZ:IHIZ,ILO:IHI) from the right.
			If WANTZ = .FALSE., then Z is unreferenced.

	   LDZ

		     LDZ is integer scalar
			LDA is the leading dimension of Z just as declared in
			the calling procedure. LDZ.GE.N.

	   V

		     V is DOUBLE PRECISION array of size (LDV,NSHFTS/2)

	   LDV

		     LDV is integer scalar
			LDV is the leading dimension of V as declared in the
			calling procedure.  LDV.GE.3.

	   U

		     U is DOUBLE PRECISION array of size
			(LDU,3*NSHFTS-3)

	   LDU

		     LDU is integer scalar
			LDU is the leading dimension of U just as declared in the
			in the calling subroutine.  LDU.GE.3*NSHFTS-3.

	   NH

		     NH is integer scalar
			NH is the number of columns in array WH available for
			workspace. NH.GE.1.

	   WH

		     WH is DOUBLE PRECISION array of size (LDWH,NH)

	   LDWH

		     LDWH is integer scalar
			Leading dimension of WH just as declared in the
			calling procedure.  LDWH.GE.3*NSHFTS-3.

	   NV

		     NV is integer scalar
			NV is the number of rows in WV agailable for workspace.
			NV.GE.1.

	   WV

		     WV is DOUBLE PRECISION array of size
			(LDWV,3*NSHFTS-3)

	   LDWV

		     LDWV is integer scalar
			LDWV is the leading dimension of WV as declared in the
			in the calling subroutine.  LDWV.GE.NV.

       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

       References:
	   K. Braman, R. Byers and R. Mathias, The Multi-Shift QR Algorithm Part I: Maintaining
	   Well Focused Shifts, and Level 3 Performance, SIAM Journal of Matrix Analysis, volume
	   23, pages 929--947, 2002.

       Definition at line 258 of file dlaqr5.f.

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

Version 3.4.2				 Tue Sep 25 2012			      dlaqr5.f(3)


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