CLAQR5 performs a single small-bulge multi-shift QR sweep.
CLAQR5 called by CLAQR0 performs a single small-bulge multi-shift QR sweep.
WANTT is LOGICAL WANTT = .true. if the triangular Schur factor is being computed. WANTT is set to .false. otherwise.
WANTZ is LOGICAL WANTZ = .true. if the unitary Schur factor is being computed. WANTZ is set to .false. otherwise.
KACC22 is INTEGER with value 0, 1, or 2. Specifies the computation mode of far-from-diagonal orthogonal updates. = 0: CLAQR5 does not accumulate reflections and does not use matrix-matrix multiply to update far-from-diagonal matrix entries. = 1: CLAQR5 accumulates reflections and uses matrix-matrix multiply to update the far-from-diagonal matrix entries. = 2: CLAQR5 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 is INTEGER N is the order of the Hessenberg matrix H upon which this subroutine operates.
KTOP is INTEGER
KBOT is INTEGER 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 is INTEGER NSHFTS gives the number of simultaneous shifts. NSHFTS must be positive and even.
S is COMPLEX array, dimension (NSHFTS) S contains the shifts of origin that define the multi- shift QR sweep. On output S may be reordered.
H is COMPLEX array, dimension (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 is INTEGER LDH is the leading dimension of H just as declared in the calling procedure. LDH.GE.MAX(1,N).
ILOZ is INTEGER
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,IHIZ) If WANTZ = .TRUE., then the QR Sweep unitary similarity transformation is accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. If WANTZ = .FALSE., then Z is unreferenced.
LDZ is INTEGER LDA is the leading dimension of Z just as declared in the calling procedure. LDZ.GE.N.
V is COMPLEX array, dimension (LDV,NSHFTS/2)
LDV is INTEGER LDV is the leading dimension of V as declared in the calling procedure. LDV.GE.3.
U is COMPLEX array, dimension (LDU,3*NSHFTS-3)
LDU is INTEGER LDU is the leading dimension of U just as declared in the in the calling subroutine. LDU.GE.3*NSHFTS-3.
NH is INTEGER NH is the number of columns in array WH available for workspace. NH.GE.1.
WH is COMPLEX array, dimension (LDWH,NH)
LDWH is INTEGER Leading dimension of WH just as declared in the calling procedure. LDWH.GE.3*NSHFTS-3.
NV is INTEGER NV is the number of rows in WV agailable for workspace. NV.GE.1.
WV is COMPLEX array, dimension (LDWV,3*NSHFTS-3)
LDWV is INTEGER LDWV is the leading dimension of WV as declared in the in the calling subroutine. LDWV.GE.NV.
Univ. of California Berkeley
Univ. of Colorado Denver
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