DLAEIN uses inverse iteration to find a right or left eigenvector
 corresponding to the eigenvalue (WR,WI) of a real upper Hessenberg
 matrix H.

          RIGHTV is LOGICAL
          = .TRUE. : compute right eigenvector;
          = .FALSE.: compute left eigenvector.

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

          N is INTEGER
          The order of the matrix H.  N >= 0.

          H is DOUBLE PRECISION array, dimension (LDH,N)
          The upper Hessenberg matrix H.

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

          WR is DOUBLE PRECISION

          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 is DOUBLE PRECISION array, dimension (N)

          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 is DOUBLE PRECISION array, dimension (LDB,N)

          LDB is INTEGER
          The leading dimension of the array B.  LDB >= N+1.

          WORK is DOUBLE PRECISION array, dimension (N)

          EPS3 is DOUBLE PRECISION
          A small machine-dependent value which is used to perturb
          close eigenvalues, and to replace zero pivots.

          SMLNUM is DOUBLE PRECISION
          A machine-dependent value close to the underflow threshold.

          BIGNUM is DOUBLE PRECISION
          A machine-dependent value close to the overflow threshold.

          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.