dlaqr3.f (3) Linux Manual Page

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 quasi-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.

WANTZ

 WANTZ 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.

N

 N is INTEGER

 The order of the matrix H and (if WANTZ is .TRUE.) the

 order of the orthogonal matrix Z.

KTOP

 KTOP is INTEGER

 It is assumed that either KTOP = 1 or H(KTOP,KTOP-1)=0.

 KBOT and KTOP together determine an isolated block

 along the diagonal of the Hessenberg matrix.

KBOT

 KBOT 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.

NW

 NW is INTEGER

 Deflation window size. 1 .LE. NW .LE. (KBOT-KTOP+1).

H

 H is DOUBLE PRECISION array, dimension (LDH,N)

 On input the initial N-by-N 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.

LDH

 LDH is integer

 Leading dimension of H just as declared in the calling

 subroutine. N .LE. LDH

ILOZ

 ILOZ is INTEGER

IHIZ

 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.

Z

 Z 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.

LDZ

 LDZ is integer

 The leading dimension of Z just as declared in the

 calling subroutine. 1 .LE. LDZ.

NS

 NS is integer

 The number of unconverged (ie approximate) eigenvalues

 returned in SR and SI that may be used as shifts by the

 calling subroutine.

ND

 ND is integer

 The number of converged eigenvalues uncovered by this

 subroutine.

SR

 SR is DOUBLE PRECISION array, dimension (KBOT)

SI

 SI 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(KBOT-ND-NS+1) through SR(KBOT-ND) and

 SI(KBOT-ND-NS+1) through SI(KBOT-ND), respectively.

 The real and imaginary parts of converged eigenvalues

 are stored in SR(KBOT-ND+1) through SR(KBOT) and

 SI(KBOT-ND+1) through SI(KBOT), respectively.

V

 V is DOUBLE PRECISION array, dimension (LDV,NW)

 An NW-by-NW work array.

LDV

 LDV is integer scalar

 The leading dimension of V just as declared in the

 calling subroutine. NW .LE. LDV

NH

 NH is integer scalar

 The number of columns of T. NH.GE.NW.

T

 T is DOUBLE PRECISION array, dimension (LDT,NW)

LDT

 LDT is integer

 The leading dimension of T just as declared in the

 calling subroutine. NW .LE. LDT

NV

 NV is integer

 The number of rows of work array WV available for

 workspace. NV.GE.NW.

WV

 WV is DOUBLE PRECISION array, dimension (LDWV,NW)

LDWV

 LDWV is integer

 The leading dimension of W just as declared in the

 calling subroutine. NW .LE. LDV

WORK

 WORK 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.

LWORK

 LWORK 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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