.TH "slaqr5.f" 3 "Wed Oct 15 2014" "Version 3.4.2" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME slaqr5.f \- .SH SYNOPSIS .br .PP .SS "Functions/Subroutines" .in +1c .ti -1c .RI "subroutine \fBslaqr5\fP (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)" .br .RI "\fI\fBSLAQR5\fP performs a single small-bulge multi-shift QR sweep\&. \fP" .in -1c .SH "Function/Subroutine Documentation" .PP .SS "subroutine slaqr5 (logicalWANTT, logicalWANTZ, integerKACC22, integerN, integerKTOP, integerKBOT, integerNSHFTS, real, dimension( * )SR, real, dimension( * )SI, real, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, real, dimension( ldz, * )Z, integerLDZ, real, dimension( ldv, * )V, integerLDV, real, dimension( ldu, * )U, integerLDU, integerNV, real, dimension( ldwv, * )WV, integerLDWV, integerNH, real, dimension( ldwh, * )WH, integerLDWH)" .PP \fBSLAQR5\fP performs a single small-bulge multi-shift QR sweep\&. .PP \fBPurpose: \fP .RS 4 .PP .nf SLAQR5, called by SLAQR0, performs a single small-bulge multi-shift QR sweep. .fi .PP .RE .PP \fBParameters:\fP .RS 4 \fIWANTT\fP .PP .nf WANTT is logical scalar WANTT = .true. if the quasi-triangular Schur factor is being computed. WANTT is set to .false. otherwise. .fi .PP .br \fIWANTZ\fP .PP .nf WANTZ is logical scalar WANTZ = .true. if the orthogonal Schur factor is being computed. WANTZ is set to .false. otherwise. .fi .PP .br \fIKACC22\fP .PP .nf KACC22 is integer with value 0, 1, or 2. Specifies the computation mode of far-from-diagonal orthogonal updates. = 0: SLAQR5 does not accumulate reflections and does not use matrix-matrix multiply to update far-from-diagonal matrix entries. = 1: SLAQR5 accumulates reflections and uses matrix-matrix multiply to update the far-from-diagonal matrix entries. = 2: SLAQR5 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. .fi .PP .br \fIN\fP .PP .nf N is integer scalar N is the order of the Hessenberg matrix H upon which this subroutine operates. .fi .PP .br \fIKTOP\fP .PP .nf KTOP is integer scalar .fi .PP .br \fIKBOT\fP .PP .nf 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. .fi .PP .br \fINSHFTS\fP .PP .nf NSHFTS is integer scalar NSHFTS gives the number of simultaneous shifts. NSHFTS must be positive and even. .fi .PP .br \fISR\fP .PP .nf SR is REAL array of size (NSHFTS) .fi .PP .br \fISI\fP .PP .nf SI is 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. On output SR and SI may be reordered. .fi .PP .br \fIH\fP .PP .nf H is 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 isolated diagonal block in rows and columns KTOP through KBOT. .fi .PP .br \fILDH\fP .PP .nf LDH is integer scalar LDH is the leading dimension of H just as declared in the calling procedure. LDH.GE.MAX(1,N). .fi .PP .br \fIILOZ\fP .PP .nf ILOZ is INTEGER .fi .PP .br \fIIHIZ\fP .PP .nf 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 .fi .PP .br \fIZ\fP .PP .nf Z is 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. .fi .PP .br \fILDZ\fP .PP .nf LDZ is integer scalar LDA is the leading dimension of Z just as declared in the calling procedure. LDZ.GE.N. .fi .PP .br \fIV\fP .PP .nf V is REAL array of size (LDV,NSHFTS/2) .fi .PP .br \fILDV\fP .PP .nf LDV is integer scalar LDV is the leading dimension of V as declared in the calling procedure. LDV.GE.3. .fi .PP .br \fIU\fP .PP .nf U is REAL array of size (LDU,3*NSHFTS-3) .fi .PP .br \fILDU\fP .PP .nf 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. .fi .PP .br \fINH\fP .PP .nf NH is integer scalar NH is the number of columns in array WH available for workspace. NH.GE.1. .fi .PP .br \fIWH\fP .PP .nf WH is REAL array of size (LDWH,NH) .fi .PP .br \fILDWH\fP .PP .nf LDWH is integer scalar Leading dimension of WH just as declared in the calling procedure. LDWH.GE.3*NSHFTS-3. .fi .PP .br \fINV\fP .PP .nf NV is integer scalar NV is the number of rows in WV agailable for workspace. NV.GE.1. .fi .PP .br \fIWV\fP .PP .nf WV is REAL array of size (LDWV,3*NSHFTS-3) .fi .PP .br \fILDWV\fP .PP .nf LDWV is integer scalar LDWV is the leading dimension of WV as declared in the in the calling subroutine. LDWV.GE.NV. .fi .PP .RE .PP \fBAuthor:\fP .RS 4 Univ\&. of Tennessee .PP Univ\&. of California Berkeley .PP Univ\&. of Colorado Denver .PP NAG Ltd\&. .RE .PP \fBDate:\fP .RS 4 September 2012 .RE .PP \fBContributors: \fP .RS 4 Karen Braman and Ralph Byers, Department of Mathematics, University of Kansas, USA .RE .PP \fBReferences: \fP .RS 4 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\&. .RE .PP .PP Definition at line 258 of file slaqr5\&.f\&. .SH "Author" .PP Generated automatically by Doxygen for LAPACK from the source code\&.