ESMF_DLAQR5 Subroutine

subroutine ESMF_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)

\brief \b ESMF_DLAQR5 performs a single small-bulge multi-shift QR sweep. \htmlonly Download ESMF_DLAQR5 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

ESMF_DLAQR5, called by ESMF_DLAQR0, performs a single small-bulge multi-shift QR sweep. \endverbatim \param[in] WANTT \verbatim WANTT is LOGICAL WANTT = .true. if the quasi-triangular Schur factor is being computed. WANTT is set to .false. otherwise. \endverbatim

\param[in] WANTZ \verbatim WANTZ is LOGICAL WANTZ = .true. if the orthogonal Schur factor is being computed. WANTZ is set to .false. otherwise. \endverbatim

\param[in] KACC22 \verbatim KACC22 is INTEGER with value 0, 1, or 2. Specifies the computation mode of far-from-diagonal orthogonal updates. = 0: ESMF_DLAQR5 does not accumulate reflections and does not use matrix-matrix multiply to update far-from-diagonal matrix entries. = 1: ESMF_DLAQR5 accumulates reflections and uses matrix-matrix multiply to update the far-from-diagonal matrix entries. = 2: ESMF_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. \endverbatim

\param[in] N \verbatim N is INTEGER N is the order of the Hessenberg matrix H upon which this subroutine operates. \endverbatim

\param[in] KTOP \verbatim KTOP is INTEGER \endverbatim

\param[in] KBOT \verbatim 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. \endverbatim

\param[in] NSHFTS \verbatim NSHFTS is INTEGER NSHFTS gives the number of simultaneous shifts. NSHFTS must be positive and even. \endverbatim

\param[in,out] SR \verbatim SR is DOUBLE PRECISION array, dimension (NSHFTS) \endverbatim

\param[in,out] SI \verbatim SI is DOUBLE PRECISION array, dimension (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. \endverbatim

\param[in,out] H \verbatim H is DOUBLE PRECISION 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. \endverbatim

\param[in] LDH \verbatim LDH is INTEGER LDH is the leading dimension of H just as declared in the calling procedure. LDH.GE.MAX(1,N). \endverbatim

\param[in] ILOZ \verbatim ILOZ is INTEGER \endverbatim

\param[in] IHIZ \verbatim 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 \endverbatim

\param[in,out] Z \verbatim Z is DOUBLE PRECISION array, dimension (LDZ,IHIZ) If WANTZ = .TRUE., then the QR Sweep orthogonal similarity transformation is accumulated into Z(ILOZ:IHIZ,ILOZ:IHIZ) from the right. If WANTZ = .FALSE., then Z is unreferenced. \endverbatim

\param[in] LDZ \verbatim LDZ is INTEGER LDA is the leading dimension of Z just as declared in the calling procedure. LDZ.GE.N. \endverbatim

\param[out] V \verbatim V is DOUBLE PRECISION array, dimension (LDV,NSHFTS/2) \endverbatim

\param[in] LDV \verbatim LDV is INTEGER LDV is the leading dimension of V as declared in the calling procedure. LDV.GE.3. \endverbatim

\param[out] U \verbatim U is DOUBLE PRECISION array, dimension (LDU,3*NSHFTS-3) \endverbatim

\param[in] LDU \verbatim LDU is INTEGER LDU is the leading dimension of U just as declared in the in the calling subroutine. LDU.GE.3*NSHFTS-3. \endverbatim

\param[in] NH \verbatim NH is INTEGER NH is the number of columns in array WH available for workspace. NH.GE.1. \endverbatim

\param[out] WH \verbatim WH is DOUBLE PRECISION array, dimension (LDWH,NH) \endverbatim

\param[in] LDWH \verbatim LDWH is INTEGER Leading dimension of WH just as declared in the calling procedure. LDWH.GE.3*NSHFTS-3. \endverbatim

\param[in] NV \verbatim NV is INTEGER NV is the number of rows in WV agailable for workspace. NV.GE.1. \endverbatim

\param[out] WV \verbatim WV is DOUBLE PRECISION array, dimension (LDWV,3*NSHFTS-3) \endverbatim

\param[in] LDWV \verbatim LDWV is INTEGER LDWV is the leading dimension of WV as declared in the in the calling subroutine. LDWV.GE.NV. \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date June 2016 \ingroup doubleOTHERauxiliary \par Contributors:

  Karen Braman and Ralph Byers, Department of Mathematics,
  University of Kansas, USA

\par 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.

Arguments