

 
Manual Reference Pages  ZLAHQR2 (l)
NAME
ZLAHQR2  i an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI
CONTENTS
Synopsis
Purpose
Arguments
Further Details
SYNOPSIS
SUBROUTINE ZLAHQR2(

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
ZLAHQR2 is an auxiliary routine called by ZHSEQR to update the eigenvalues and Schur decomposition already computed by ZHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI. This version of ZLAHQR (not the standard LAPACK version) uses a
doubleshift algorithm (like LAPACK’s DLAHQR).
Unlike the standard LAPACK convention, this does not assume the
subdiagonal is real, nor does it work to preserve this quality if
given.
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 required;
= .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,ILO1) = 0 (unless ILO = 1).
ZLAHQR 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) 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. 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
eigenvalues 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, 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*(IHIILO+1)
iterations; elements i+1:ihi of W contain those
eigenvalues which have been successfully computed.


FURTHER DETAILS
Modified by Mark R. Fahey, June, 2000
ScaLAPACK version 1.7  ZLAHQR2 (l)  13 August 2001 
Visit the GSP FreeBSD Man Page Interface. Output converted with manServer 1.07. 