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Man Pages


Manual Reference Pages  -  CLAHQR2 (l)

NAME

CLAHQR2 - i an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by CHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI

CONTENTS

Synopsis
Purpose
Arguments
Further Details

SYNOPSIS

SUBROUTINE CLAHQR2( 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 H( LDH, * ), W( * ), Z( LDZ, * )

PURPOSE

CLAHQR2 is an auxiliary routine called by CHSEQR to update the eigenvalues and Schur decomposition already computed by CHSEQR, by dealing with the Hessenberg submatrix in rows and columns ILO to IHI. This version of CLAHQR (not the standard LAPACK version) uses a
double-shift algorithm (like LAPACK’s SLAHQR).
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,ILO-1) = 0 (unless ILO = 1). CLAHQR 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 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 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 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, CLAHQR 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.

FURTHER DETAILS

Modified by Mark R. Fahey, June, 2000

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ScaLAPACK version 1.7 CLAHQR2 (l) 13 August 2001

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