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

```slaein.f(3)							      LAPACK							       slaein.f(3)

NAME
slaein.f -

SYNOPSIS
Functions/Subroutines
subroutine slaein (RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO)
SLAEIN computes 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

NAG Ltd.

Date:
September 2012

Definition at line 172 of file slaein.f.

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

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

## Check Out this Related Man Page

```SLAEIN(l)								 )								 SLAEIN(l)

NAME
SLAEIN  -  use  inverse	iteration  to  find a right or left eigenvector corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg
matrix H

SYNOPSIS
SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI, B, LDB, WORK, EPS3, SMLNUM, BIGNUM, INFO )

LOGICAL	  NOINIT, RIGHTV

INTEGER	  INFO, LDB, LDH, N

REAL 	  BIGNUM, EPS3, SMLNUM, WI, WR

REAL 	  B( LDB, * ), H( LDH, * ), VI( * ), VR( * ), WORK( * )

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.

ARGUMENTS
RIGHTV	(input) LOGICAL
= .TRUE. : compute right eigenvector;
= .FALSE.: compute left eigenvector.

NOINIT	(input) LOGICAL
= .TRUE. : no initial vector supplied in (VR,VI).
= .FALSE.: initial vector supplied in (VR,VI).

N       (input) INTEGER
The order of the matrix H.  N >= 0.

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

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

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

VR      (input/output) REAL array, dimension (N)
VI      (input/output) 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 imagi-
nary 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       (workspace) REAL array, dimension (LDB,N)

LDB     (input) INTEGER
The leading dimension of the array B.  LDB >= N+1.

WORK   (workspace) REAL array, dimension (N)

EPS3    (input) REAL
A small machine-dependent value which is used to perturb close eigenvalues, and to replace zero pivots.

SMLNUM  (input) REAL
A machine-dependent value close to the underflow threshold.

BIGNUM  (input) REAL
A machine-dependent value close to the overflow threshold.

INFO    (output) 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.

LAPACK version 3.0						   15 June 2000 							 SLAEIN(l)```