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# dlaein.f(3) [centos man page]

```dlaein.f(3)							      LAPACK							       dlaein.f(3)

NAME
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

NAG Ltd.

Date:
September 2012

Definition at line 172 of file dlaein.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       dlaein.f(3)```

## Check Out this Related Man Page

```zlaein.f(3)							      LAPACK							       zlaein.f(3)

NAME
zlaein.f -

SYNOPSIS
Functions/Subroutines
subroutine zlaein (RIGHTV, NOINIT, N, H, LDH, W, V, B, LDB, RWORK, EPS3, SMLNUM, INFO)
ZLAEIN

Function/Subroutine Documentation
subroutine zlaein (logicalRIGHTV, logicalNOINIT, integerN, complex*16, dimension( ldh, * )H, integerLDH, complex*16W, complex*16, dimension( *
)V, complex*16, dimension( ldb, * )B, integerLDB, double precision, dimension( * )RWORK, double precisionEPS3, double precisionSMLNUM,
integerINFO)
ZLAEIN

Purpose:

ZLAEIN 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*16 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*16
The eigenvalue of H whose corresponding right or left
eigenvector is to be computed.

V

V is COMPLEX*16 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*16 array, dimension (LDB,N)

LDB

LDB is INTEGER
The leading dimension of the array B.  LDB >= max(1,N).

RWORK

RWORK 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.

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

NAG Ltd.

Date:
November 2011

Definition at line 149 of file zlaein.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       zlaein.f(3)```