DLAQR5
November 2010
This auxiliary subroutine called by DLAQR0 performs a
single small-bulge multi-shift QR sweep.
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
computed. 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: DLAQR5 does not accumulate reflections and does not
use matrix-matrix multiply to update far-from-diagonal
matrix entries.
= 1: DLAQR5 accumulates reflections and uses matrix-matrix
multiply to update the far-from-diagonal matrix entries.
= 2: DLAQR5 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
subroutine 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/output) DOUBLE PRECISION array of size (NSHFTS)
SI (input/output) DOUBLE PRECISION 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. On output SR and SI may be
reordered.
H (input/output) DOUBLE PRECISION 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 isolated 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
calling 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) DOUBLE PRECISION 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 calling procedure. LDZ.GE.N.
V (workspace) DOUBLE PRECISION 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) DOUBLE PRECISION 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.
WH (workspace) DOUBLE PRECISION array of size (LDWH,NH)
LDWH (input) integer scalar
Leading dimension of WH just as declared in the
calling procedure. LDWH.GE.3*NSHFTS-3.
NV (input) integer scalar
NV is the number of rows in WV agailable for workspace.
NV.GE.1.
WV (workspace) DOUBLE PRECISION 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.
This auxiliary subroutine called by DLAQR0 performs a
single small-bulge multi-shift QR sweep.
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
computed. 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: DLAQR5 does not accumulate reflections and does not
use matrix-matrix multiply to update far-from-diagonal
matrix entries.
= 1: DLAQR5 accumulates reflections and uses matrix-matrix
multiply to update the far-from-diagonal matrix entries.
= 2: DLAQR5 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
subroutine 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/output) DOUBLE PRECISION array of size (NSHFTS)
SI (input/output) DOUBLE PRECISION 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. On output SR and SI may be
reordered.
H (input/output) DOUBLE PRECISION 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 isolated 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
calling 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) DOUBLE PRECISION 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 calling procedure. LDZ.GE.N.
V (workspace) DOUBLE PRECISION 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) DOUBLE PRECISION 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.
WH (workspace) DOUBLE PRECISION array of size (LDWH,NH)
LDWH (input) integer scalar
Leading dimension of WH just as declared in the
calling procedure. LDWH.GE.3*NSHFTS-3.
NV (input) integer scalar
NV is the number of rows in WV agailable for workspace.
NV.GE.1.
WV (workspace) DOUBLE PRECISION 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.