# zlaein.f man page

zlaein.f

## Synopsis

### Functions/Subroutines

subroutine zlaein (RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3, SMLNUM, INFO)
ZLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

## Function/Subroutine Documentation

### subroutine zlaein (logical RIGHTV, logical NOINIT, integer N, complex*16, dimension( ldh, * ) H, integer LDH, complex*16 W, complex*16, dimension( * ) V, complex*16, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) RWORK, double precision EPS3, double precision SMLNUM, integer INFO)

ZLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

Purpose:

``` ZLAEIN uses inverse iteration to find a right or left eigenvector
corresponding to the eigenvalue W of a complex upper Hessenberg
matrix H.```
Parameters:

RIGHTV

```          RIGHTV is LOGICAL
= .TRUE. : compute right eigenvector;
= .FALSE.: compute left eigenvector.```

NOINIT

```          NOINIT is LOGICAL
= .TRUE. : no initial vector supplied in V
= .FALSE.: initial vector supplied in V.```

N

```          N is INTEGER
The order of the matrix H.  N >= 0.```

H

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

LDH

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

W

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

V

```          V is 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

`          B is COMPLEX*16 array, dimension (LDB,N)`

LDB

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

RWORK

`          RWORK is DOUBLE PRECISION array, dimension (N)`

EPS3

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

SMLNUM

```          SMLNUM is DOUBLE PRECISION
A machine-dependent value close to the underflow threshold.```

INFO

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

Definition at line 151 of file zlaein.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zlaein(3) is an alias of zlaein.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK