zlahqr(3)

NAME

ZLAHQR - i an auxiliary routine called by ZHSEQR to update

the eigenvalues and Schur decomposition already computed by ZHSE

QR, by dealing with the Hessenberg submatrix in rows and columns

ILO to IHI

SYNOPSIS

SUBROUTINE  ZLAHQR(  WANTT, WANTZ, N, ILO, IHI, H, LDH, W,
ILOZ, IHIZ, Z, LDZ, INFO )
    LOGICAL        WANTT, WANTZ
    INTEGER        IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
    COMPLEX*16     H( LDH, * ), W( * ), Z( LDZ, * )

PURPOSE

ZLAHQR is an auxiliary routine called by ZHSEQR to update

the eigenvalues and Schur decomposition already computed by ZHSE

QR, by dealing with the Hessenberg submatrix in rows and columns

ILO to IHI.

ARGUMENTS

WANTT (input) LOGICAL

= .TRUE. : the full Schur form T is required;
= .FALSE.: only eigenvalues are required.

WANTZ (input) LOGICAL

= .TRUE. : the matrix of Schur vectors Z is re

quired;
= .FALSE.: Schur vectors are not required.

N (input) INTEGER

The order of the matrix H. N >= 0.

ILO (input) INTEGER

IHI (input) INTEGER It is assumed that H is

already upper triangular in rows and columns IHI+1:N, and that

H(ILO,ILO-1) = 0 (unless ILO = 1). ZLAHQR works primarily with

the Hessenberg submatrix in rows and columns ILO to IHI, but ap

plies transformations to all of H if WANTT is .TRUE.. 1 <= ILO

<= max(1,IHI); IHI <= N.

H (input/output) COMPLEX*16 array, dimension (LDH,N)

On entry, the upper Hessenberg matrix H. On exit,

if WANTT is .TRUE., H is upper triangular in rows and columns

ILO:IHI, with any 2-by-2 diagonal blocks in standard form. If

WANTT is .FALSE., the contents of H are unspecified on exit.

LDH (input) INTEGER

The leading dimension of the array H. LDH >=

max(1,N).

W (output) COMPLEX*16 array, dimension (N)

The computed eigenvalues ILO to IHI are stored in

the corresponding elements of W. If WANTT is .TRUE., the eigen

values are stored in the same order as on the diagonal of the

Schur form returned in H, with W(i) = H(i,i).

ILOZ (input) INTEGER

IHIZ (input) INTEGER Specify the rows of Z to

which transformations must be applied if WANTZ is .TRUE.. 1 <=

ILOZ <= ILO; IHI <= IHIZ <= N.

Z (input/output) COMPLEX*16 array, dimension (LDZ,N)

If WANTZ is .TRUE., on entry Z must contain the

current matrix Z of transformations accumulated by ZHSEQR, and on

exit Z has been updated; transformations are applied only to the

submatrix Z(ILOZ:IHIZ,ILO:IHI). If WANTZ is .FALSE., Z is not

referenced.

LDZ (input) INTEGER

The leading dimension of the array Z. LDZ >=

max(1,N).

INFO (output) INTEGER

= 0: successful exit
> 0: if INFO = i, ZLAHQR failed to compute all the

eigenvalues ILO to IHI in a total of 30*(IHI-ILO+1) iterations;

elements i+1:ihi of W contain those eigenvalues which have been

successfully computed.

LAPACK version 3.0 15 June 2000

ZLAHQR(3)