SLAEIN uses inverse iteration to find a right or left eigenvector


 corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg


 matrix H.

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012