# dlaein.f man page

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 (logical RIGHTV, logical NOINIT, integer N, double precision, dimension( ldh, * ) H, integer LDH, double precision WR, double precision WI, double precision, dimension( * ) VR, double precision, dimension( * ) VI, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( * ) WORK, double precision EPS3, double precision SMLNUM, double precision BIGNUM, integer INFO)

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

NAG Ltd.

Date:

December 2016

Definition at line 174 of file dlaein.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

Tue Nov 14 2017 Version 3.8.0 LAPACK