SLAQR6(3) ScaLAPACK routine of NEC Numeric Library Collection SLAQR6(3)
NAME
SLAQR6 - performs a single small-bulge multi-shift QR sweep, moving the
chain of bulges from top to bottom in the submatrix
H(KTOP:KBOT,KTOP:KBOT), collecting the transformations in the matrix HV
*or* accumulating the transformations in the matrix Z (see below)
SYNOPSIS
SUBROUTINE SLAQR6( JOB, 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 )
CHARACTER JOB
INTEGER IHIZ, ILOZ, KACC22, KBOT, KTOP, LDH, LDU, LDV,
LDWH, LDWV, LDZ, N, NH, NSHFTS, NV
LOGICAL WANTT, WANTZ
REAL H( LDH, * ), SI( * ), SR( * ), U( LDU, * ), V( LDV,
* ), WH( LDWH, * ), WV( LDWV, * ), Z( LDZ, * )
PURPOSE
This auxiliary subroutine called by PDLAQR5 performs a single small-
bulge multi-shift QR sweep, moving the chain of bulges from top to bot-
tom in the submatrix H(KTOP:KBOT,KTOP:KBOT), collecting the transforma-
tions in the matrix HV *or* accumulating the transformations in the
matrix Z (see below).
ARGUMENTS
JOB (input) CHARACTER scalar
Set the kind of job to do in SLAQR6, as follows:
JOB = 'I': Introduce and chase bulges in submatrix
JOB = 'C': Chase bulges from top to bottom of submatrix
JOB = 'O': Chase bulges off submatrix
WANTT (input) LOGICAL scalar
WANTT = .true. if the quasi-triangular Schur factor is being
computed. WANTT is set to .false. otherwise.
WANTZ (input) LOGICAL scalar
WANTZ = .true. if the orthogonal Schur factor is being com-
puted. WANTZ is set to .false. otherwise.
KACC22 (input) INTEGER with value 0, 1, or 2.
Specifies the computation mode of far-from-diagonal orthogonal
updates.
= 0: SLAQR6 does not accumulate reflections and does not
use matrix-matrix multiply to update far-from-diagonal
matrix entries.
= 1: SLAQR6 accumulates reflections and uses matrix-matrix
multiply to update the far-from-diagonal matrix entries.
= 2: SLAQR6 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 (input) INTEGER scalar
N is the order of the Hessenberg matrix H upon which this sub-
routine operates.
KTOP (input) INTEGER scalar
KBOT (input) 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 (input) integer scalar
NSHFTS gives the number of simultaneous shifts. NSHFTS must be
positive and even.
SR (input) REAL array of size (NSHFTS)
SI (input) REAL 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.
H (input/output) REAL 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 iso-
lated diagonal block in rows and columns KTOP through KBOT.
LDH (input) integer scalar
LDH is the leading dimension of H just as declared in the call-
ing procedure. LDH.GE.MAX(1,N).
ILOZ (input) INTEGER
IHIZ (input) 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) REAL 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 (input) integer scalar
LDA is the leading dimension of Z just as declared in the call-
ing procedure. LDZ.GE.N.
V (workspace) REAL array of size (LDV,NSHFTS/2)
LDV (input) integer scalar
LDV is the leading dimension of V as declared in the calling
procedure. LDV.GE.3.
U (workspace) REAL array of size (LDU,3*NSHFTS-3)
LDU (input) integer scalar
LDU is the leading dimension of U just as declared in the in
the calling subroutine. LDU.GE.3*NSHFTS-3.
NH (input) integer scalar
NH is the number of columns in array WH available for
workspace. NH.GE.1 is required for usage of this workspace,
otherwise the updates of the far-from-diagonal elements will be
updated without level 3 BLAS.
WH (workspace) REAL array of size (LDWH,NH)
LDWH (input) integer scalar
Leading dimension of WH just as declared in the calling proce-
dure. LDWH.GE.3*NSHFTS-3.
NV (input) integer scalar
NV is the number of rows in WV agailable for workspace.
NV.GE.1 is required for usage of this workspace, otherwise the
updates of the far-from-diagonal elements will be updated with-
out level 3 BLAS.
WV (workspace) REAL array of size (LDWV,3*NSHFTS-3)
LDWV (input) integer scalar
LDWV is the leading dimension of WV as declared in the in the
calling subroutine. LDWV.GE.NV.
ScaLAPACK routine 31 October 2017 SLAQR6(3)