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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 (logicalRIGHTV, logicalNOINIT, integerN, complex*16, dimension( ldh, * )H, integerLDH, complex*16W, complex*16, dimension( * )V, complex*16, dimension( ldb, * )B, integerLDB, double precision, dimension( * )RWORK, double precisionEPS3, double precisionSMLNUM, integerINFO)

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:
September 2012
Definition at line 149 of file zlaein.f.

# Author

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