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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: uses inverse iteration to find a right or left eigenvector corresponding to the eigenvalue W of a complex upper

```NAME
LAPACK-3  -  uses inverse iteration to find a right or left eigenvector
corresponding to the eigenvalue W of a complex upper Hessenberg  matrix
H

SYNOPSIS
SUBROUTINE ZLAEIN( RIGHTV,  NOINIT,  N,  H,  LDH,  W, V, B, LDB, RWORK,
EPS3, SMLNUM, INFO )

LOGICAL        NOINIT, RIGHTV

INTEGER        INFO, LDB, LDH, N

DOUBLE         PRECISION EPS3, SMLNUM

COMPLEX*16     W

DOUBLE         PRECISION RWORK( * )

COMPLEX*16     B( LDB, * ), H( LDH, * ), V( * )

PURPOSE
ZLAEIN uses inverse iteration to  find  a  right  or  left  eigenvector
corresponding  to the eigenvalue W of a complex 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 V
= .FALSE.: initial vector supplied in V.

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

H       (input) COMPLEX*16 array, dimension (LDH,N)
The upper Hessenberg matrix H.

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

W       (input) COMPLEX*16
The eigenvalue of H whose corresponding right or left
eigenvector is to be computed.

V       (input/output) COMPLEX*16 array, dimension (N)
On entry, if NOINIT = .FALSE., V must contain a starting
vector for inverse iteration; otherwise V need not be set.
On exit, V contains the computed eigenvector, 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|.

B       (workspace) COMPLEX*16 array, dimension (LDB,N)

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

RWORK   (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.

INFO    (output) INTEGER
= 0:  successful exit
= 1:  inverse iteration did not converge; V is set to the
last iterate.

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
```

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