1SLAEIN(1)           LAPACK auxiliary routine (version 3.1)           SLAEIN(1)
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NAME

6       SLAEIN  -  inverse iteration to find a right or left eigenvector corre‐
7       sponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
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SYNOPSIS

10       SUBROUTINE SLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,  B,  LDB,
11                          WORK, EPS3, SMLNUM, BIGNUM, INFO )
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13           LOGICAL        NOINIT, RIGHTV
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15           INTEGER        INFO, LDB, LDH, N
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17           REAL           BIGNUM, EPS3, SMLNUM, WI, WR
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19           REAL           B(  LDB, * ), H( LDH, * ), VI( * ), VR( * ), WORK( *
20                          )
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PURPOSE

23       SLAEIN uses inverse iteration to find a right or left eigenvector  cor‐
24       responding  to the eigenvalue (WR,WI) of a real upper Hessenberg matrix
25       H.
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ARGUMENTS

29       RIGHTV   (input) LOGICAL
30                = .TRUE. : compute right eigenvector;
31                = .FALSE.: compute left eigenvector.
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33       NOINIT   (input) LOGICAL
34                = .TRUE. : no initial vector supplied in (VR,VI).
35                = .FALSE.: initial vector supplied in (VR,VI).
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37       N       (input) INTEGER
38               The order of the matrix H.  N >= 0.
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40       H       (input) REAL array, dimension (LDH,N)
41               The upper Hessenberg matrix H.
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43       LDH     (input) INTEGER
44               The leading dimension of the array H.  LDH >= max(1,N).
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46       WR      (input) REAL
47               WI      (input) REAL The real and imaginary parts of the eigen‐
48               value  of H whose corresponding right or left eigenvector is to
49               be computed.
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51       VR      (input/output) REAL array, dimension (N)
52               VI      (input/output) REAL array, dimension (N) On  entry,  if
53               NOINIT  = .FALSE. and WI = 0.0, VR must contain a real starting
54               vector for inverse iteration using the real eigenvalue  WR;  if
55               NOINIT = .FALSE. and WI.ne.0.0, VR and VI must contain the real
56               and imaginary parts of a complex starting  vector  for  inverse
57               iteration  using  the  complex eigenvalue (WR,WI); otherwise VR
58               and VI need not be set.  On exit, if WI = 0.0  (real  eigenval‐
59               ue),  VR  contains  the computed real eigenvector; if WI.ne.0.0
60               (complex eigenvalue), VR and VI contain the real and  imaginary
61               parts  of  the computed complex eigenvector. The eigenvector is
62               normalized so that the component of largest magnitude has  mag‐
63               nitude 1; here the magnitude of a complex number (x,y) is taken
64               to be |x| + |y|.  VI is not referenced if WI = 0.0.
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66       B       (workspace) REAL array, dimension (LDB,N)
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68       LDB     (input) INTEGER
69               The leading dimension of the array B.  LDB >= N+1.
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71       WORK   (workspace) REAL array, dimension (N)
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73       EPS3    (input) REAL
74               A small machine-dependent value which is used to perturb  close
75               eigenvalues, and to replace zero pivots.
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77       SMLNUM  (input) REAL
78               A machine-dependent value close to the underflow threshold.
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80       BIGNUM  (input) REAL
81               A machine-dependent value close to the overflow threshold.
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83       INFO    (output) INTEGER
84               = 0:  successful exit
85               = 1:  inverse iteration did not converge; VR is set to the last
86               iterate, and so is VI if WI.ne.0.0.
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90 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLAEIN(1)