dlaqr5.f (3) Linux Manual Page

dlaqr5.f –

Synopsis

Functions/Subroutines

subroutine dlaqr5 (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)
DLAQR5 performs a single small-bulge multi-shift QR sweep.

Function/Subroutine Documentation

subroutine dlaqr5 (logicalWANTT, logicalWANTZ, integerKACC22, integerN, integerKTOP, integerKBOT, integerNSHFTS, double precision, dimension( * )SR, double precision, dimension( * )SI, double precision, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, double precision, dimension( ldz, * )Z, integerLDZ, double precision, dimension( ldv, * )V, integerLDV, double precision, dimension( ldu, * )U, integerLDU, integerNV, double precision, dimension( ldwv, * )WV, integerLDWV, integerNH, double precision, dimension( ldwh, * )WH, integerLDWH)

DLAQR5 performs a single small-bulge multi-shift QR sweep.

Purpose:

 DLAQR5, called by DLAQR0, performs a

 single small-bulge multi-shift QR sweep.

 

Parameters:

WANTT

 WANTT is logical scalar

 WANTT = .true. if the quasi-triangular Schur factor

 is being computed. WANTT is set to .false. otherwise.

WANTZ

 WANTZ is logical scalar

 WANTZ = .true. if the orthogonal 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: 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

 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.

SR

 SR is DOUBLE PRECISION array of size (NSHFTS)

SI

 SI is 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

 H is 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

 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

 Z is 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

 LDZ is integer scalar

 LDA is the leading dimension of Z just as declared in

 the calling procedure. LDZ.GE.N.

V

 V is DOUBLE PRECISION 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

 U is DOUBLE PRECISION 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

 NH is integer scalar

 NH is the number of columns in array WH available for

 workspace. NH.GE.1.

WH

 WH is DOUBLE PRECISION 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

 NV is integer scalar

 NV is the number of rows in WV agailable for workspace.

 NV.GE.1.

WV

 WV is DOUBLE PRECISION 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 258 of file dlaqr5.f.

Author

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