
zlaqr3.f(3) LAPACK zlaqr3.f(3)
NAME
zlaqr3.f 
SYNOPSIS
Functions/Subroutines
subroutine zlaqr3 (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)
ZLAQR3 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 zlaqr3 (logicalWANTT, logicalWANTZ, integerN, integerKTOP, integerKBOT, integerNW,
complex*16, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, complex*16,
dimension( ldz, * )Z, integerLDZ, integerNS, integerND, complex*16, dimension( * )SH,
complex*16, dimension( ldv, * )V, integerLDV, integerNH, complex*16, dimension( ldt, * )T,
integerLDT, integerNV, complex*16, dimension( ldwv, * )WV, integerLDWV, complex*16,
dimension( * )WORK, integerLWORK)
ZLAQR3 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:
ZLAQR3 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,KTOP1)=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. (KBOTKTOP+1).
H
H is COMPLEX*16 array, dimension (LDH,N)
On input the initial NbyN 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*16 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*16 array, dimension KBOT
On output, approximate eigenvalues that may
be used for shifts are stored in SH(KBOTNDNS+1)
through SR(KBOTND). Converged eigenvalues are
stored in SH(KBOTND+1) through SH(KBOT).
V
V is COMPLEX*16 array, dimension (LDV,NW)
An NWbyNW 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*16 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*16 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*16 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; ZLAQR3
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 266 of file zlaqr3.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 zlaqr3.f(3) 
