Unix/Linux Go Back    


CentOS 7.0 - man page for claqr3.f (centos section 3)

Linux & Unix Commands - Search Man Pages
Man Page or Keyword Search:   man
Select Man Page Set:       apropos Keyword Search (sections above)


claqr3.f(3)				      LAPACK				      claqr3.f(3)

NAME
       claqr3.f -

SYNOPSIS
   Functions/Subroutines
       subroutine claqr3 (WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND,
	   SH, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK)
	   CLAQR3 performs the unitary 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 claqr3 (logicalWANTT, logicalWANTZ, integerN, integerKTOP, integerKBOT, integerNW,
       complex, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, complex, dimension(
       ldz, * )Z, integerLDZ, integerNS, integerND, complex, dimension( * )SH, complex,
       dimension( ldv, * )V, integerLDV, integerNH, complex, dimension( ldt, * )T, integerLDT,
       integerNV, complex, dimension( ldwv, * )WV, integerLDWV, complex, dimension( * )WORK,
       integerLWORK)
       CLAQR3 performs the unitary 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:

	       CLAQR3 accepts as input an upper Hessenberg matrix
	       H and performs an unitary 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 unitary 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 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 unitary matrix Z is updated so
		     so that the unitary 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 unitary 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 COMPLEX 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 a unitary
		     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 COMPLEX array, dimension (LDZ,N)
		     IF WANTZ is .TRUE., then on output, the unitary
		     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.

	   SH

		     SH is COMPLEX array, dimension KBOT
		     On output, approximate eigenvalues that may
		     be used for shifts are stored in SH(KBOT-ND-NS+1)
		     through SR(KBOT-ND).  Converged eigenvalues are
		     stored in SH(KBOT-ND+1) through SH(KBOT).

	   V

		     V is COMPLEX 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 COMPLEX 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 COMPLEX 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 COMPLEX 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; CLAQR3
		     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 265 of file claqr3.f.

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

Version 3.4.2				 Tue Sep 25 2012			      claqr3.f(3)
Unix & Linux Commands & Man Pages : ©2000 - 2018 Unix and Linux Forums


All times are GMT -4. The time now is 09:01 PM.