zlaqr3 (3)  Linux Manuals
NAME
zlaqr3.f 
SYNOPSIS
Functions/Subroutines
subroutine zlaqr3 (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)
ZLAQR3 performs the unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).
Function/Subroutine Documentation
subroutine zlaqr3 (logicalWANTT, logicalWANTZ, integerN, integerKTOP, integerKBOT, integerNW, complex*16, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, complex*16, dimension( ldz, * )Z, integerLDZ, integerNS, integerND, complex*16, dimension( * )SH, complex*16, dimension( ldv, * )V, integerLDV, integerNH, complex*16, dimension( ldt, * )T, integerLDT, integerNV, complex*16, dimension( ldwv, * )WV, integerLDWV, complex*16, dimension( * )WORK, integerLWORK)
ZLAQR3 performs the unitary similarity transformation of a Hessenberg matrix to detect and deflate fully converged eigenvalues from a trailing principal submatrix (aggressive early deflation).
Purpose:

Aggressive early deflation: ZLAQR3 accepts as input an upper Hessenberg matrix H and performs an unitary similarity transformation designed to detect and deflate fully converged eigenvalues from a trailing principal submatrix. On output H has been over written by a new Hessenberg matrix that is a perturbation of an unitary similarity transformation of H. It is to be hoped that the final version of H has many zero subdiagonal entries.
Parameters:

WANTT
WANTT is LOGICAL If .TRUE., then the Hessenberg matrix H is fully updated so that the triangular Schur factor may be computed (in cooperation with the calling subroutine). If .FALSE., then only enough of H is updated to preserve the eigenvalues.
WANTZWANTZ is LOGICAL If .TRUE., then the unitary matrix Z is updated so so that the unitary Schur factor may be computed (in cooperation with the calling subroutine). If .FALSE., then Z is not referenced.
NN is INTEGER The order of the matrix H and (if WANTZ is .TRUE.) the order of the unitary matrix Z.
KTOPKTOP is INTEGER It is assumed that either KTOP = 1 or H(KTOP,KTOP1)=0. KBOT and KTOP together determine an isolated block along the diagonal of the Hessenberg matrix.
KBOTKBOT is INTEGER It is assumed without a check that either KBOT = N or H(KBOT+1,KBOT)=0. KBOT and KTOP together determine an isolated block along the diagonal of the Hessenberg matrix.
NWNW is INTEGER Deflation window size. 1 .LE. NW .LE. (KBOTKTOP+1).
HH is COMPLEX*16 array, dimension (LDH,N) On input the initial NbyN section of H stores the Hessenberg matrix undergoing aggressive early deflation. On output H has been transformed by a unitary similarity transformation, perturbed, and the returned to Hessenberg form that (it is to be hoped) has some zero subdiagonal entries.
LDHLDH is integer Leading dimension of H just as declared in the calling subroutine. N .LE. LDH
ILOZILOZ is INTEGER
IHIZIHIZ is INTEGER Specify the rows of Z to which transformations must be applied if WANTZ is .TRUE.. 1 .LE. ILOZ .LE. IHIZ .LE. N.
ZZ is COMPLEX*16 array, dimension (LDZ,N) IF WANTZ is .TRUE., then on output, the unitary similarity transformation mentioned above has been accumulated into Z(ILOZ:IHIZ,ILO:IHI) from the right. If WANTZ is .FALSE., then Z is unreferenced.
LDZLDZ is integer The leading dimension of Z just as declared in the calling subroutine. 1 .LE. LDZ.
NSNS is integer The number of unconverged (ie approximate) eigenvalues returned in SR and SI that may be used as shifts by the calling subroutine.
NDND is integer The number of converged eigenvalues uncovered by this subroutine.
SHSH is COMPLEX*16 array, dimension KBOT On output, approximate eigenvalues that may be used for shifts are stored in SH(KBOTNDNS+1) through SR(KBOTND). Converged eigenvalues are stored in SH(KBOTND+1) through SH(KBOT).
VV is COMPLEX*16 array, dimension (LDV,NW) An NWbyNW work array.
LDVLDV is integer scalar The leading dimension of V just as declared in the calling subroutine. NW .LE. LDV
NHNH is integer scalar The number of columns of T. NH.GE.NW.
TT is COMPLEX*16 array, dimension (LDT,NW)
LDTLDT is integer The leading dimension of T just as declared in the calling subroutine. NW .LE. LDT
NVNV is integer The number of rows of work array WV available for workspace. NV.GE.NW.
WVWV is COMPLEX*16 array, dimension (LDWV,NW)
LDWVLDWV is integer The leading dimension of W just as declared in the calling subroutine. NW .LE. LDV
WORKWORK is COMPLEX*16 array, dimension LWORK. On exit, WORK(1) is set to an estimate of the optimal value of LWORK for the given values of N, NW, KTOP and KBOT.
LWORKLWORK is integer The dimension of the work array WORK. LWORK = 2*NW suffices, but greater efficiency may result from larger values of LWORK. If LWORK = 1, then a workspace query is assumed; ZLAQR3 only estimates the optimal workspace size for the given values of N, NW, KTOP and KBOT. The estimate is returned in WORK(1). No error message related to LWORK is issued by XERBLA. Neither H nor Z are accessed.
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
Definition at line 266 of file zlaqr3.f.
Author
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