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# dlaein

```
NAME
DLAEIN - use inverse iteration to find a right or left
eigenvector corresponding to the eigenvalue (WR,WI) of a
real upper Hessenberg matrix H

SYNOPSIS
SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR,
VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM,
INFO )

LOGICAL        NOINIT, RIGHTV

INTEGER        INFO, LDB, LDH, N

DOUBLE         PRECISION BIGNUM, EPS3, SMLNUM, WI, WR

DOUBLE         PRECISION B( LDB, * ), H( LDH, * ), VI( *
), VR( * ), WORK( * )

PURPOSE
DLAEIN uses inverse iteration to find a right or left eigen-
vector corresponding to the eigenvalue (WR,WI) of a real
upper Hessenberg matrix H.

ARGUMENTS
RIGHTV   (input) LOGICAL
= .TRUE. : compute right eigenvector;
= .FALSE.: compute left eigenvector.

NOINIT   (input) LOGICAL
= .TRUE. : no initial vector supplied in (VR,VI).
= .FALSE.: initial vector supplied in (VR,VI).

N       (input) INTEGER
The order of the matrix H.  N >= 0.

H       (input) DOUBLE PRECISION array, dimension (LDH,N)
The upper Hessenberg matrix H.

LDH     (input) INTEGER
The leading dimension of the array H.  LDH >=
max(1,N).

WR      (input) DOUBLE PRECISION
WI      (input) DOUBLE PRECISION The real and ima-
ginary parts of the eigenvalue of H whose
corresponding right or left eigenvector is to be
computed.

VR      (input/output) DOUBLE PRECISION array, dimension (N)
VI      (input/output) DOUBLE PRECISION array,

dimension (N) On entry, if NOINIT = .FALSE. and WI =
0.0, VR must contain a real starting vector for
inverse iteration using the real eigenvalue WR; if
NOINIT = .FALSE. and WI.ne.0.0, VR and VI must con-
tain the real and imaginary parts of a complex
starting vector for inverse iteration using the com-
plex eigenvalue (WR,WI); otherwise VR and VI need
not be set.  On exit, if WI = 0.0 (real eigenvalue),
VR contains the computed real eigenvector; if
WI.ne.0.0 (complex eigenvalue), VR and VI contain
the real and imaginary parts of the computed complex
eigenvector. The eigenvector is normalized so that
the component of largest magnitude has magnitude 1;
here the magnitude of a complex number (x,y) is
taken to be |x| + |y|.  VI is not referenced if WI =
0.0.

B       (workspace) DOUBLE PRECISION array, dimension (LDB,N)

LDB     (input) INTEGER
The leading dimension of the array B.  LDB >= N+1.

WORK   (workspace) DOUBLE PRECISION array, dimension (N)

EPS3    (input) DOUBLE PRECISION
A small machine-dependent value which is used to
perturb close eigenvalues, and to replace zero
pivots.

SMLNUM  (input) DOUBLE PRECISION
A machine-dependent value close to the underflow
threshold.

BIGNUM  (input) DOUBLE PRECISION
A machine-dependent value close to the overflow
threshold.

INFO    (output) INTEGER
= 0:  successful exit
= 1:  inverse iteration did not converge; VR is set
to the last iterate, and so is VI if WI.ne.0.0.
```