# claein.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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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