# claein.f man page

claein.f —

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine claein (logicalRIGHTV, logicalNOINIT, integerN, complex, dimension( ldh, * )H, integerLDH, complexW, complex, dimension( * )V, complex, dimension( ldb, * )B, integerLDB, real, dimension( * )RWORK, realEPS3, realSMLNUM, integerINFO)

**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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 149 of file claein.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

claein(3) is an alias of claein.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK