# claein.f - Man Page

SRC/claein.f

## Synopsis

### Functions/Subroutines

subroutine claein (rightv, noinit, n, h, ldh, w, v, b, ldb, rwork, eps3, smlnum, info)
CLAEIN computes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

## Function/Subroutine Documentation

### subroutine claein (logical rightv, logical noinit, integer n, complex, dimension( ldh, * ) h, integer ldh, complex w, complex, dimension( * ) v, complex, dimension( ldb, * ) b, integer ldb, real, dimension( * ) rwork, real eps3, real smlnum, integer info)

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

Purpose:

``` CLAEIN 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 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
The eigenvalue of H whose corresponding right or left
eigenvector is to be computed.```

V

```          V is COMPLEX 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 array, dimension (LDB,N)`

LDB

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

RWORK

`          RWORK is REAL array, dimension (N)`

EPS3

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

SMLNUM

```          SMLNUM is REAL
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.

Definition at line 147 of file claein.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK