LAPACK  3.4.2 LAPACK: Linear Algebra PACKage
slaein.f File Reference

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

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:
 [in] RIGHTV ``` RIGHTV is LOGICAL = .TRUE. : compute right eigenvector; = .FALSE.: compute left eigenvector.``` [in] NOINIT ``` NOINIT is LOGICAL = .TRUE. : no initial vector supplied in (VR,VI). = .FALSE.: initial vector supplied in (VR,VI).``` [in] N ``` N is INTEGER The order of the matrix H. N >= 0.``` [in] H ``` H is REAL array, dimension (LDH,N) The upper Hessenberg matrix H.``` [in] LDH ``` LDH is INTEGER The leading dimension of the array H. LDH >= max(1,N).``` [in] WR ` WR is REAL` [in] WI ``` WI is REAL The real and imaginary parts of the eigenvalue of H whose corresponding right or left eigenvector is to be computed.``` [in,out] VR ` VR is REAL array, dimension (N)` [in,out] 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.``` [out] B ` B is REAL array, dimension (LDB,N)` [in] LDB ``` LDB is INTEGER The leading dimension of the array B. LDB >= N+1.``` [out] WORK ` WORK is REAL array, dimension (N)` [in] EPS3 ``` EPS3 is REAL A small machine-dependent value which is used to perturb close eigenvalues, and to replace zero pivots.``` [in] SMLNUM ``` SMLNUM is REAL A machine-dependent value close to the underflow threshold.``` [in] BIGNUM ``` BIGNUM is REAL A machine-dependent value close to the overflow threshold.``` [out] 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.```
Date:
September 2012

Definition at line 172 of file slaein.f.

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