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---
:name: dlaqr5
:md5sum: 7e0db3e70152db066243f2fdafb92b99
:category: :subroutine
:arguments:
- wantt:
:type: logical
:intent: input
- wantz:
:type: logical
:intent: input
- kacc22:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- ktop:
:type: integer
:intent: input
- kbot:
:type: integer
:intent: input
- nshfts:
:type: integer
:intent: input
- sr:
:type: doublereal
:intent: input/output
:dims:
- nshfts
- si:
:type: doublereal
:intent: input/output
:dims:
- nshfts
- h:
:type: doublereal
:intent: input/output
:dims:
- ldh
- n
- ldh:
:type: integer
:intent: input
- iloz:
:type: integer
:intent: input
- ihiz:
:type: integer
:intent: input
- z:
:type: doublereal
:intent: input/output
:dims:
- "wantz ? ldz : 0"
- "wantz ? ihiz : 0"
- ldz:
:type: integer
:intent: input
- v:
:type: doublereal
:intent: workspace
:dims:
- ldv
- nshfts/2
- ldv:
:type: integer
:intent: input
- u:
:type: doublereal
:intent: workspace
:dims:
- ldu
- 3*nshfts-3
- ldu:
:type: integer
:intent: input
- nv:
:type: integer
:intent: input
- wv:
:type: doublereal
:intent: workspace
:dims:
- ldwv
- 3*nshfts-3
- ldwv:
:type: integer
:intent: input
- nh:
:type: integer
:intent: input
- wh:
:type: doublereal
:intent: workspace
:dims:
- ldwh
- MAX(1,nh)
- ldwh:
:type: integer
:intent: input
:substitutions:
ldwh: 3*nshfts-3
ldz: n
ldwv: nv
ldu: 3*nshfts-3
ldv: "3"
:fortran_help: " 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 )\n\n\
* This auxiliary subroutine called by DLAQR0 performs a\n\
* single small-bulge multi-shift QR sweep.\n\
*\n\n\
* WANTT (input) logical scalar\n\
* WANTT = .true. if the quasi-triangular Schur factor\n\
* is being computed. WANTT is set to .false. otherwise.\n\
*\n\
* WANTZ (input) logical scalar\n\
* WANTZ = .true. if the orthogonal Schur factor is being\n\
* computed. WANTZ is set to .false. otherwise.\n\
*\n\
* KACC22 (input) integer with value 0, 1, or 2.\n\
* Specifies the computation mode of far-from-diagonal\n\
* orthogonal updates.\n\
* = 0: DLAQR5 does not accumulate reflections and does not\n\
* use matrix-matrix multiply to update far-from-diagonal\n\
* matrix entries.\n\
* = 1: DLAQR5 accumulates reflections and uses matrix-matrix\n\
* multiply to update the far-from-diagonal matrix entries.\n\
* = 2: DLAQR5 accumulates reflections, uses matrix-matrix\n\
* multiply to update the far-from-diagonal matrix entries,\n\
* and takes advantage of 2-by-2 block structure during\n\
* matrix multiplies.\n\
*\n\
* N (input) integer scalar\n\
* N is the order of the Hessenberg matrix H upon which this\n\
* subroutine operates.\n\
*\n\
* KTOP (input) integer scalar\n\
* KBOT (input) integer scalar\n\
* These are the first and last rows and columns of an\n\
* isolated diagonal block upon which the QR sweep is to be\n\
* applied. It is assumed without a check that\n\
* either KTOP = 1 or H(KTOP,KTOP-1) = 0\n\
* and\n\
* either KBOT = N or H(KBOT+1,KBOT) = 0.\n\
*\n\
* NSHFTS (input) integer scalar\n\
* NSHFTS gives the number of simultaneous shifts. NSHFTS\n\
* must be positive and even.\n\
*\n\
* SR (input/output) DOUBLE PRECISION array of size (NSHFTS)\n\
* SI (input/output) DOUBLE PRECISION array of size (NSHFTS)\n\
* SR contains the real parts and SI contains the imaginary\n\
* parts of the NSHFTS shifts of origin that define the\n\
* multi-shift QR sweep. On output SR and SI may be\n\
* reordered.\n\
*\n\
* H (input/output) DOUBLE PRECISION array of size (LDH,N)\n\
* On input H contains a Hessenberg matrix. On output a\n\
* multi-shift QR sweep with shifts SR(J)+i*SI(J) is applied\n\
* to the isolated diagonal block in rows and columns KTOP\n\
* through KBOT.\n\
*\n\
* LDH (input) integer scalar\n\
* LDH is the leading dimension of H just as declared in the\n\
* calling procedure. LDH.GE.MAX(1,N).\n\
*\n\
* ILOZ (input) INTEGER\n\
* IHIZ (input) INTEGER\n\
* Specify the rows of Z to which transformations must be\n\
* applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N\n\
*\n\
* Z (input/output) DOUBLE PRECISION array of size (LDZ,IHI)\n\
* If WANTZ = .TRUE., then the QR Sweep orthogonal\n\
* similarity transformation is accumulated into\n\
* Z(ILOZ:IHIZ,ILO:IHI) from the right.\n\
* If WANTZ = .FALSE., then Z is unreferenced.\n\
*\n\
* LDZ (input) integer scalar\n\
* LDA is the leading dimension of Z just as declared in\n\
* the calling procedure. LDZ.GE.N.\n\
*\n\
* V (workspace) DOUBLE PRECISION array of size (LDV,NSHFTS/2)\n\
*\n\
* LDV (input) integer scalar\n\
* LDV is the leading dimension of V as declared in the\n\
* calling procedure. LDV.GE.3.\n\
*\n\
* U (workspace) DOUBLE PRECISION array of size\n\
* (LDU,3*NSHFTS-3)\n\
*\n\
* LDU (input) integer scalar\n\
* LDU is the leading dimension of U just as declared in the\n\
* in the calling subroutine. LDU.GE.3*NSHFTS-3.\n\
*\n\
* NH (input) integer scalar\n\
* NH is the number of columns in array WH available for\n\
* workspace. NH.GE.1.\n\
*\n\
* WH (workspace) DOUBLE PRECISION array of size (LDWH,NH)\n\
*\n\
* LDWH (input) integer scalar\n\
* Leading dimension of WH just as declared in the\n\
* calling procedure. LDWH.GE.3*NSHFTS-3.\n\
*\n\
* NV (input) integer scalar\n\
* NV is the number of rows in WV agailable for workspace.\n\
* NV.GE.1.\n\
*\n\
* WV (workspace) DOUBLE PRECISION array of size\n\
* (LDWV,3*NSHFTS-3)\n\
*\n\
* LDWV (input) integer scalar\n\
* LDWV is the leading dimension of WV as declared in the\n\
* in the calling subroutine. LDWV.GE.NV.\n\
*\n\n\
* ================================================================\n\
* Based on contributions by\n\
* Karen Braman and Ralph Byers, Department of Mathematics,\n\
* University of Kansas, USA\n\
*\n\
* ================================================================\n\
* Reference:\n\
*\n\
* K. Braman, R. Byers and R. Mathias, The Multi-Shift QR\n\
* Algorithm Part I: Maintaining Well Focused Shifts, and\n\
* Level 3 Performance, SIAM Journal of Matrix Analysis,\n\
* volume 23, pages 929--947, 2002.\n\
*\n\
* ================================================================\n"
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