1DLAEIN(1)           LAPACK auxiliary routine (version 3.1)           DLAEIN(1)
2
3
4

NAME

6       DLAEIN  -  inverse iteration to find a right or left eigenvector corre‐
7       sponding to the eigenvalue (WR,WI) of a real upper Hessenberg matrix H
8

SYNOPSIS

10       SUBROUTINE DLAEIN( RIGHTV, NOINIT, N, H, LDH, WR, WI, VR, VI,  B,  LDB,
11                          WORK, EPS3, SMLNUM, BIGNUM, INFO )
12
13           LOGICAL        NOINIT, RIGHTV
14
15           INTEGER        INFO, LDB, LDH, N
16
17           DOUBLE         PRECISION BIGNUM, EPS3, SMLNUM, WI, WR
18
19           DOUBLE         PRECISION  B(  LDB, * ), H( LDH, * ), VI( * ), VR( *
20                          ), WORK( * )
21

PURPOSE

23       DLAEIN 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.
26
27

ARGUMENTS

29       RIGHTV   (input) LOGICAL
30                = .TRUE. : compute right eigenvector;
31                = .FALSE.: compute left eigenvector.
32
33       NOINIT   (input) LOGICAL
34                = .TRUE. : no initial vector supplied in (VR,VI).
35                = .FALSE.: initial vector supplied in (VR,VI).
36
37       N       (input) INTEGER
38               The order of the matrix H.  N >= 0.
39
40       H       (input) DOUBLE PRECISION array, dimension (LDH,N)
41               The upper Hessenberg matrix H.
42
43       LDH     (input) INTEGER
44               The leading dimension of the array H.  LDH >= max(1,N).
45
46       WR      (input) DOUBLE PRECISION
47               WI      (input) DOUBLE PRECISION The real and  imaginary  parts
48               of the eigenvalue of H whose corresponding right or left eigen‐
49               vector is to be computed.
50
51       VR      (input/output) DOUBLE PRECISION array, dimension (N)
52               VI      (input/output) DOUBLE PRECISION array, dimension (N) On
53               entry, if NOINIT = .FALSE. and WI = 0.0, VR must contain a real
54               starting vector for inverse iteration using the real eigenvalue
55               WR;  if  NOINIT = .FALSE. and WI.ne.0.0, VR and VI must contain
56               the real and imaginary parts of a complex starting  vector  for
57               inverse  iteration using the complex eigenvalue (WR,WI); other‐
58               wise VR and VI need not be set.  On exit, if WI = 0.0 (real ei‐
59               genvalue),  VR  contains  the  computed  real  eigenvector;  if
60               WI.ne.0.0 (complex eigenvalue), VR and VI contain the real  and
61               imaginary parts of the computed complex eigenvector. The eigen‐
62               vector is normalized so that the component of largest magnitude
63               has  magnitude  1; here the magnitude of a complex number (x,y)
64               is taken to be |x| + |y|.  VI is not referenced if WI = 0.0.
65
66       B       (workspace) DOUBLE PRECISION array, dimension (LDB,N)
67
68       LDB     (input) INTEGER
69               The leading dimension of the array B.  LDB >= N+1.
70
71       WORK   (workspace) DOUBLE PRECISION array, dimension (N)
72
73       EPS3    (input) DOUBLE PRECISION
74               A small machine-dependent value which is used to perturb  close
75               eigenvalues, and to replace zero pivots.
76
77       SMLNUM  (input) DOUBLE PRECISION
78               A machine-dependent value close to the underflow threshold.
79
80       BIGNUM  (input) DOUBLE PRECISION
81               A machine-dependent value close to the overflow threshold.
82
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.
87
88
89
90 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       DLAEIN(1)