# dlaein (3) - Linux Manuals

dlaein.f -

## SYNOPSIS

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine dlaein (logicalRIGHTV, logicalNOINIT, integerN, double precision, dimension( ldh, * )H, integerLDH, double precisionWR, double precisionWI, double precision, dimension( * )VR, double precision, dimension( * )VI, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( * )WORK, double precisionEPS3, double precisionSMLNUM, double precisionBIGNUM, integerINFO)

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

Purpose:

``` DLAEIN 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 DOUBLE PRECISION 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 DOUBLE PRECISION
```

WI

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

VR

```          VR is DOUBLE PRECISION array, dimension (N)
```

VI

```          VI is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDB,N)
```

LDB

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

WORK

```          WORK 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.
```

BIGNUM

```          BIGNUM is DOUBLE PRECISION
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