claqr3-f(3)

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

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

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

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

 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

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