1SLAEIN(1)           LAPACK auxiliary routine (version 3.2)           SLAEIN(1)
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NAME

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

11       SUBROUTINE SLAEIN( RIGHTV,  NOINIT,  N, H, LDH, WR, WI, VR, VI, B, LDB,
12                          WORK, EPS3, SMLNUM, BIGNUM, INFO )
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14           LOGICAL        NOINIT, RIGHTV
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16           INTEGER        INFO, LDB, LDH, N
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18           REAL           BIGNUM, EPS3, SMLNUM, WI, WR
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20           REAL           B( LDB, * ), H( LDH, * ), VI( * ), VR( * ), WORK(  *
21                          )
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PURPOSE

24       SLAEIN  uses inverse iteration to find a right or left eigenvector cor‐
25       responding to the eigenvalue (WR,WI) of a real upper Hessenberg  matrix
26       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.e2m)ber 2008                       SLAEIN(1)