SLAQR2(3) LAPACK routine of NEC Numeric Library Collection SLAQR2(3)
NAME
SLAQR2
SYNOPSIS
SUBROUTINE SLAQR2 (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)
PURPOSE
SLAQR2 is identical to SLAQR3 except that it avoids
recursion by calling SLAHQR instead of SLAQR4.
Aggressive early deflation:
This subroutine 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.
ARGUMENTS
WANTT (input)
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 (input)
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 (input)
N is INTEGER
The order of the matrix H and (if WANTZ is .TRUE.) the
order of the orthogonal matrix Z.
KTOP (input)
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 (input)
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 (input)
NW is INTEGER
Deflation window size. 1 .LE. NW .LE. (KBOT-KTOP+1).
H (input/output)
H is REAL 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 (input)
LDH is integer
Leading dimension of H just as declared in the calling
subroutine. N .LE. LDH
ILOZ (input)
ILOZ is INTEGER
IHIZ (input)
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 (input/output)
Z is REAL 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 (input)
LDZ is integer
The leading dimension of Z just as declared in the
calling subroutine. 1 .LE. LDZ.
NS (output)
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 (output)
ND is integer
The number of converged eigenvalues uncovered by this
subroutine.
SR (output)
SR is REAL array, dimension KBOT
SI (output)
SI is REAL 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 (output)
V is REAL array, dimension (LDV,NW)
An NW-by-NW work array.
LDV (input)
LDV is integer scalar
The leading dimension of V just as declared in the
calling subroutine. NW .LE. LDV
NH (input)
NH is integer scalar
The number of columns of T. NH.GE.NW.
T (output)
T is REAL array, dimension (LDT,NW)
LDT (input)
LDT is integer
The leading dimension of T just as declared in the
calling subroutine. NW .LE. LDT
NV (input)
NV is integer
The number of rows of work array WV available for
workspace. NV.GE.NW.
WV (output)
WV is REAL array, dimension (LDWV,NW)
LDWV (input)
LDWV is integer
The leading dimension of W just as declared in the
calling subroutine. NW .LE. LDV
WORK (output)
WORK is REAL 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 (input)
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; SLAQR2
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.
LAPACK routine 31 October 2017 SLAQR2(3)