claqr5-f(3)

claqr5.f –

Synopsis

Functions/Subroutines

subroutine claqr5 (WANTT, WANTZ, KACC22, N, KTOP, KBOT, NSHFTS, S, H, LDH, ILOZ, IHIZ, Z, LDZ, V, LDV, U, LDU, NV, WV, LDWV, NH, WH, LDWH)
CLAQR5 performs a single small-bulge multi-shift QR sweep.

Function/Subroutine Documentation

subroutine claqr5 (logicalWANTT, logicalWANTZ, integerKACC22, integerN, integerKTOP, integerKBOT, integerNSHFTS, complex, dimension( * )S, complex, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( ldv, * )V, integerLDV, complex, dimension( ldu, * )U, integerLDU, integerNV, complex, dimension( ldwv, * )WV, integerLDWV, integerNH, complex, dimension( ldwh, * )WH, integerLDWH)

CLAQR5 performs a single small-bulge multi-shift QR sweep.

Purpose:

 CLAQR5 called by CLAQR0 performs a
 single small-bulge multi-shift QR sweep.

Parameters:

WANTT

 WANTT is logical scalar
 WANTT = .true. if the triangular Schur factor
 is being computed. WANTT is set to .false. otherwise.

WANTZ

 WANTZ is logical scalar
 WANTZ = .true. if the unitary Schur factor is being
 computed. WANTZ is set to .false. otherwise.

KACC22

 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 scalar
 N is the order of the Hessenberg matrix H upon which this
 subroutine operates.

KTOP

 KTOP is integer scalar

KBOT

 KBOT is 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

 NSHFTS is integer scalar
 NSHFTS gives the number of simultaneous shifts. NSHFTS
 must be positive and even.

 S is COMPLEX array of size (NSHFTS)
 S contains the shifts of origin that define the multi-
 shift QR sweep. On output S may be reordered.

 H is COMPLEX 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

 LDH is integer scalar
 LDH is the leading dimension of H just as declared in the
 calling procedure. LDH.GE.MAX(1,N).

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 is COMPLEX array of size (LDZ,IHI)
 If WANTZ = .TRUE., then the QR Sweep unitary
 similarity transformation is accumulated into
 Z(ILOZ:IHIZ,ILO:IHI) from the right.
 If WANTZ = .FALSE., then Z is unreferenced.

LDZ

 LDZ is integer scalar
 LDA is the leading dimension of Z just as declared in
 the calling procedure. LDZ.GE.N.

 V is COMPLEX array of size (LDV,NSHFTS/2)

LDV

 LDV is integer scalar
 LDV is the leading dimension of V as declared in the
 calling procedure. LDV.GE.3.

 U is COMPLEX array of size
 (LDU,3*NSHFTS-3)

LDU

 LDU is integer scalar
 LDU is the leading dimension of U just as declared in the
 in the calling subroutine. LDU.GE.3*NSHFTS-3.

 NH is integer scalar
 NH is the number of columns in array WH available for
 workspace. NH.GE.1.

 WH is COMPLEX array of size (LDWH,NH)

LDWH

 LDWH is integer scalar
 Leading dimension of WH just as declared in the
 calling procedure. LDWH.GE.3*NSHFTS-3.

 NV is integer scalar
 NV is the number of rows in WV agailable for workspace.
 NV.GE.1.

 WV is COMPLEX array of size
 (LDWV,3*NSHFTS-3)

LDWV

 LDWV is integer scalar
 LDWV is the leading dimension of WV as declared in the
 in the calling subroutine. LDWV.GE.NV.

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

References:

K. Braman, R. Byers and R. Mathias, The Multi-Shift QR Algorithm Part I: Maintaining Well Focused Shifts, and Level 3 Performance, SIAM Journal of Matrix Analysis, volume 23, pages 929–947, 2002.

Definition at line 250 of file claqr5.f.

Author

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