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

6       ZLAEIN  -  inverse iteration to find a right or left eigenvector corre‐
7       sponding to the eigenvalue W of a complex upper Hessenberg matrix H
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SYNOPSIS

10       SUBROUTINE ZLAEIN( RIGHTV, NOINIT, N, H, LDH,  W,  V,  B,  LDB,  RWORK,
11                          EPS3, SMLNUM, INFO )
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13           LOGICAL        NOINIT, RIGHTV
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15           INTEGER        INFO, LDB, LDH, N
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17           DOUBLE         PRECISION EPS3, SMLNUM
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19           COMPLEX*16     W
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21           DOUBLE         PRECISION RWORK( * )
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23           COMPLEX*16     B( LDB, * ), H( LDH, * ), V( * )
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PURPOSE

26       ZLAEIN  uses inverse iteration to find a right or left eigenvector cor‐
27       responding to the eigenvalue W of a complex upper Hessenberg matrix H.
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ARGUMENTS

31       RIGHTV   (input) LOGICAL
32                = .TRUE. : compute right eigenvector;
33                = .FALSE.: compute left eigenvector.
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35       NOINIT   (input) LOGICAL
36                = .TRUE. : no initial vector supplied in V
37                = .FALSE.: initial vector supplied in V.
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39       N       (input) INTEGER
40               The order of the matrix H.  N >= 0.
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42       H       (input) COMPLEX*16 array, dimension (LDH,N)
43               The upper Hessenberg matrix H.
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45       LDH     (input) INTEGER
46               The leading dimension of the array H.  LDH >= max(1,N).
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48       W       (input) COMPLEX*16
49               The eigenvalue of H whose corresponding right or left eigenvec‐
50               tor is to be computed.
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52       V       (input/output) COMPLEX*16 array, dimension (N)
53               On entry, if NOINIT = .FALSE., V must contain a starting vector
54               for inverse iteration; otherwise V need not be set.  On exit, V
55               contains  the computed eigenvector, normalized so that the com‐
56               ponent of largest magnitude has magnitude 1; here the magnitude
57               of a complex number (x,y) is taken to be |x| + |y|.
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59       B       (workspace) COMPLEX*16 array, dimension (LDB,N)
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61       LDB     (input) INTEGER
62               The leading dimension of the array B.  LDB >= max(1,N).
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64       RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
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66       EPS3    (input) DOUBLE PRECISION
67               A  small machine-dependent value which is used to perturb close
68               eigenvalues, and to replace zero pivots.
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70       SMLNUM  (input) DOUBLE PRECISION
71               A machine-dependent value close to the underflow threshold.
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73       INFO    (output) INTEGER
74               = 0:  successful exit
75               = 1:  inverse iteration did not converge; V is set to the  last
76               iterate.
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80 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       ZLAEIN(1)
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