slahqr(3)

NAME

SLAHQR - i an auxiliary routine called by SHSEQR to update

the eigenvalues and Schur decomposition already computed by SHSE

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

ILO to IHI

SYNOPSIS

SUBROUTINE  SLAHQR( WANTT, WANTZ, N, ILO, IHI, H, LDH, WR,
WI, ILOZ, IHIZ, Z, LDZ, INFO )
    LOGICAL        WANTT, WANTZ
    INTEGER        IHI, IHIZ, ILO, ILOZ, INFO, LDH, LDZ, N
    REAL            H( LDH, * ), WI( * ), WR( * ), Z( LDZ,
* )

PURPOSE

SLAHQR is an auxiliary routine called by SHSEQR to update

the eigenvalues and Schur decomposition already computed by SHSE

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 quasi-triangular in rows and columns IHI+1:N, and

that H(ILO,ILO-1) = 0 (unless ILO = 1). SLAHQR works primarily

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

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

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

H (input/output) REAL array, dimension (LDH,N)

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

if WANTT is .TRUE., H is upper quasi-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).

WR (output) REAL array, dimension (N)

WI (output) REAL array, dimension (N) The re

al and imaginary parts, respectively, of the computed eigenvalues

ILO to IHI are stored in the corresponding elements of WR and WI.

If two eigenvalues are computed as a complex conjugate pair, they

are stored in consecutive elements of WR and WI, say the i-th and

(i+1)th, with WI(i) > 0 and WI(i+1) < 0. If WANTT is .TRUE., the

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

the Schur form returned in H, with WR(i) = H(i,i), and, if

H(i:i+1,i:i+1) is a 2-by-2 diagonal block, WI(i) =

sqrt(H(i+1,i)*H(i,i+1)) and WI(i+1) = -WI(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) REAL array, dimension (LDZ,N)

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

current matrix Z of transformations accumulated by SHSEQR, 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: SLAHQR failed to compute all the eigenvalues

ILO to IHI in a total of 30*(IHI-ILO+1) iterations; if INFO = i,

elements i+1:ihi of WR and WI contain those eigenvalues which

have been successfully computed.

FURTHER DETAILS

2-96 Based on modifications by

David Day, Sandia National Laboratory, USA

LAPACK version 3.0 15 June 2000

SLAHQR(3)