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---
:name: zlaqr2
:md5sum: ffeac35e8baa8da04e2b19326ee08e26
:category: :subroutine
:arguments:
- wantt:
:type: logical
:intent: input
- wantz:
:type: logical
:intent: input
- n:
:type: integer
:intent: input
- ktop:
:type: integer
:intent: input
- kbot:
:type: integer
:intent: input
- nw:
:type: integer
:intent: input
- h:
:type: doublecomplex
:intent: input/output
:dims:
- ldh
- n
- ldh:
:type: integer
:intent: input
- iloz:
:type: integer
:intent: input
- ihiz:
:type: integer
:intent: input
- z:
:type: doublecomplex
:intent: input/output
:dims:
- ldz
- n
- ldz:
:type: integer
:intent: input
- ns:
:type: integer
:intent: output
- nd:
:type: integer
:intent: output
- sh:
:type: doublecomplex
:intent: output
:dims:
- MAX(1,kbot)
- v:
:type: doublecomplex
:intent: workspace
:dims:
- ldv
- MAX(1,nw)
- ldv:
:type: integer
:intent: input
- nh:
:type: integer
:intent: input
- t:
:type: doublecomplex
:intent: workspace
:dims:
- ldv
- MAX(1,nw)
- ldt:
:type: integer
:intent: input
- nv:
:type: integer
:intent: input
- wv:
:type: doublecomplex
:intent: workspace
:dims:
- ldv
- MAX(1,nw)
- ldwv:
:type: integer
:intent: input
- work:
:type: doublecomplex
:intent: workspace
:dims:
- MAX(1,lwork)
- lwork:
:type: integer
:intent: input
:option: true
:default: 2*nw
:substitutions:
ldwv: nw
ldt: nw
ldv: nw
:fortran_help: " SUBROUTINE ZLAQR2( WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND, SH, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK )\n\n\
* This subroutine is identical to ZLAQR3 except that it avoids\n\
* recursion by calling ZLAHQR instead of ZLAQR4.\n\
*\n\
*\n\
* ******************************************************************\n\
* Aggressive early deflation:\n\
*\n\
* This subroutine accepts as input an upper Hessenberg matrix\n\
* H and performs an unitary similarity transformation\n\
* designed to detect and deflate fully converged eigenvalues from\n\
* a trailing principal submatrix. On output H has been over-\n\
* written by a new Hessenberg matrix that is a perturbation of\n\
* an unitary similarity transformation of H. It is to be\n\
* hoped that the final version of H has many zero subdiagonal\n\
* entries.\n\
*\n\
* ******************************************************************\n\n\
* WANTT (input) LOGICAL\n\
* If .TRUE., then the Hessenberg matrix H is fully updated\n\
* so that the triangular Schur factor may be\n\
* computed (in cooperation with the calling subroutine).\n\
* If .FALSE., then only enough of H is updated to preserve\n\
* the eigenvalues.\n\
*\n\
* WANTZ (input) LOGICAL\n\
* If .TRUE., then the unitary matrix Z is updated so\n\
* so that the unitary Schur factor may be computed\n\
* (in cooperation with the calling subroutine).\n\
* If .FALSE., then Z is not referenced.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix H and (if WANTZ is .TRUE.) the\n\
* order of the unitary matrix Z.\n\
*\n\
* KTOP (input) INTEGER\n\
* It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0.\n\
* KBOT and KTOP together determine an isolated block\n\
* along the diagonal of the Hessenberg matrix.\n\
*\n\
* KBOT (input) INTEGER\n\
* It is assumed without a check that either\n\
* KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together\n\
* determine an isolated block along the diagonal of the\n\
* Hessenberg matrix.\n\
*\n\
* NW (input) INTEGER\n\
* Deflation window size. 1 .LE. NW .LE. (KBOT-KTOP+1).\n\
*\n\
* H (input/output) COMPLEX*16 array, dimension (LDH,N)\n\
* On input the initial N-by-N section of H stores the\n\
* Hessenberg matrix undergoing aggressive early deflation.\n\
* On output H has been transformed by a unitary\n\
* similarity transformation, perturbed, and the returned\n\
* to Hessenberg form that (it is to be hoped) has some\n\
* zero subdiagonal entries.\n\
*\n\
* LDH (input) integer\n\
* Leading dimension of H just as declared in the calling\n\
* subroutine. N .LE. LDH\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) COMPLEX*16 array, dimension (LDZ,N)\n\
* IF WANTZ is .TRUE., then on output, the unitary\n\
* similarity transformation mentioned above has been\n\
* accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right.\n\
* If WANTZ is .FALSE., then Z is unreferenced.\n\
*\n\
* LDZ (input) integer\n\
* The leading dimension of Z just as declared in the\n\
* calling subroutine. 1 .LE. LDZ.\n\
*\n\
* NS (output) integer\n\
* The number of unconverged (ie approximate) eigenvalues\n\
* returned in SR and SI that may be used as shifts by the\n\
* calling subroutine.\n\
*\n\
* ND (output) integer\n\
* The number of converged eigenvalues uncovered by this\n\
* subroutine.\n\
*\n\
* SH (output) COMPLEX*16 array, dimension KBOT\n\
* On output, approximate eigenvalues that may\n\
* be used for shifts are stored in SH(KBOT-ND-NS+1)\n\
* through SR(KBOT-ND). Converged eigenvalues are\n\
* stored in SH(KBOT-ND+1) through SH(KBOT).\n\
*\n\
* V (workspace) COMPLEX*16 array, dimension (LDV,NW)\n\
* An NW-by-NW work array.\n\
*\n\
* LDV (input) integer scalar\n\
* The leading dimension of V just as declared in the\n\
* calling subroutine. NW .LE. LDV\n\
*\n\
* NH (input) integer scalar\n\
* The number of columns of T. NH.GE.NW.\n\
*\n\
* T (workspace) COMPLEX*16 array, dimension (LDT,NW)\n\
*\n\
* LDT (input) integer\n\
* The leading dimension of T just as declared in the\n\
* calling subroutine. NW .LE. LDT\n\
*\n\
* NV (input) integer\n\
* The number of rows of work array WV available for\n\
* workspace. NV.GE.NW.\n\
*\n\
* WV (workspace) COMPLEX*16 array, dimension (LDWV,NW)\n\
*\n\
* LDWV (input) integer\n\
* The leading dimension of W just as declared in the\n\
* calling subroutine. NW .LE. LDV\n\
*\n\
* WORK (workspace) COMPLEX*16 array, dimension LWORK.\n\
* On exit, WORK(1) is set to an estimate of the optimal value\n\
* of LWORK for the given values of N, NW, KTOP and KBOT.\n\
*\n\
* LWORK (input) integer\n\
* The dimension of the work array WORK. LWORK = 2*NW\n\
* suffices, but greater efficiency may result from larger\n\
* values of LWORK.\n\
*\n\
* If LWORK = -1, then a workspace query is assumed; ZLAQR2\n\
* only estimates the optimal workspace size for the given\n\
* values of N, NW, KTOP and KBOT. The estimate is returned\n\
* in WORK(1). No error message related to LWORK is issued\n\
* by XERBLA. Neither H nor Z are accessed.\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"
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