# slaein.f man page

slaein.f —

## Synopsis

### Functions/Subroutines

subroutineslaein(RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO)SLAEINcomputes a specified right or left eigenvector of an upper Hessenberg matrix by inverse iteration.

## Function/Subroutine Documentation

### subroutine slaein (logicalRIGHTV, logicalNOINIT, integerN, real, dimension( ldh, * )H, integerLDH, realWR, realWI, real, dimension( * )VR, real, dimension( * )VI, real, dimension( ldb, * )B, integerLDB, real, dimension( * )WORK, realEPS3, realSMLNUM, realBIGNUM, integerINFO)

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

**Purpose:**

```
SLAEIN uses inverse iteration to find a right or left eigenvector
corresponding to the eigenvalue (WR,WI) of a real 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 (VR,VI).
= .FALSE.: initial vector supplied in (VR,VI).
```

*N*

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

*H*

```
H is REAL array, dimension (LDH,N)
The upper Hessenberg matrix H.
```

*LDH*

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

*WR*

`WR is REAL`

*WI*

```
WI is REAL
The real and imaginary parts of the eigenvalue of H whose
corresponding right or left eigenvector is to be computed.
```

*VR*

`VR is REAL array, dimension (N)`

*VI*

```
VI is REAL array, dimension (N)
On entry, if NOINIT = .FALSE. and WI = 0.0, VR must contain
a real starting vector for inverse iteration using the real
eigenvalue WR; if NOINIT = .FALSE. and WI.ne.0.0, VR and VI
must contain the real and imaginary parts of a complex
starting vector for inverse iteration using the complex
eigenvalue (WR,WI); otherwise VR and VI need not be set.
On exit, if WI = 0.0 (real eigenvalue), VR contains the
computed real eigenvector; if WI.ne.0.0 (complex eigenvalue),
VR and VI contain the real and imaginary parts of the
computed complex eigenvector. The eigenvector is 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|.
VI is not referenced if WI = 0.0.
```

*B*

`B is REAL array, dimension (LDB,N)`

*LDB*

```
LDB is INTEGER
The leading dimension of the array B. LDB >= N+1.
```

*WORK*

`WORK 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.
```

*BIGNUM*

```
BIGNUM is REAL
A machine-dependent value close to the overflow threshold.
```

*INFO*

```
INFO is INTEGER
= 0: successful exit
= 1: inverse iteration did not converge; VR is set to the
last iterate, and so is VI if WI.ne.0.0.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 172 of file slaein.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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