DLAQR3 (3)  Linux Manuals
NAME
dlaqr3.f 
SYNOPSIS
Functions/Subroutines
subroutine dlaqr3 (WANTT, WANTZ, N, KTOP, KBOT, NW, H, LDH, ILOZ, IHIZ, Z, LDZ, NS, ND, SR, SI, V, LDV, NH, T, LDT, NV, WV, LDWV, WORK, LWORK)
DLAQR3 performs the orthogonal 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 dlaqr3 (logicalWANTT, logicalWANTZ, integerN, integerKTOP, integerKBOT, integerNW, double precision, dimension( ldh, * )H, integerLDH, integerILOZ, integerIHIZ, double precision, dimension( ldz, * )Z, integerLDZ, integerNS, integerND, double precision, dimension( * )SR, double precision, dimension( * )SI, double precision, dimension( ldv, * )V, integerLDV, integerNH, double precision, dimension( ldt, * )T, integerLDT, integerNV, double precision, dimension( ldwv, * )WV, integerLDWV, double precision, dimension( * )WORK, integerLWORK)
DLAQR3 performs the orthogonal 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: DLAQR3 accepts as input an upper Hessenberg matrix H and performs an orthogonal 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 orthogonal 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 quasitriangular 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 orthogonal matrix Z is updated so so that the orthogonal 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 orthogonal 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 DOUBLE PRECISION 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 an orthogonal 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 DOUBLE PRECISION array, dimension (LDZ,N) IF WANTZ is .TRUE., then on output, the orthogonal 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.
SRSR is DOUBLE PRECISION array, dimension (KBOT)
SISI is DOUBLE PRECISION array, dimension (KBOT) On output, the real and imaginary parts of approximate eigenvalues that may be used for shifts are stored in SR(KBOTNDNS+1) through SR(KBOTND) and SI(KBOTNDNS+1) through SI(KBOTND), respectively. The real and imaginary parts of converged eigenvalues are stored in SR(KBOTND+1) through SR(KBOT) and SI(KBOTND+1) through SI(KBOT), respectively.
VV is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDWV,NW)
LDWVLDWV is integer The leading dimension of W just as declared in the calling subroutine. NW .LE. LDV
WORKWORK is DOUBLE PRECISION 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; DLAQR3 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 274 of file dlaqr3.f.
Author
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