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

6       ZLARFG  -  generates  a complex elementary reflector H of order n, such
7       that   H' * ( alpha ) = ( beta ), H' * H = I
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SYNOPSIS

10       SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU )
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12           INTEGER        INCX, N
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14           COMPLEX*16     ALPHA, TAU
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16           COMPLEX*16     X( * )
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PURPOSE

19       ZLARFG generates a complex elementary reflector H of order n, such that
20                  (   x   )   (   0  )
21       where alpha and  beta  are  scalars,  with  beta  real,  and  x  is  an
22       (n-1)-element complex vector. H is represented in the form
23             H = I - tau * ( 1 ) * ( 1 v' ) ,
24                           ( v )
25       where  tau is a complex scalar and v is a complex (n-1)-element vector.
26       Note that H is not hermitian.
27       If the elements of x are all zero and alpha is real, then tau = 0 and H
28       is taken to be the unit matrix.
29       Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .
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ARGUMENTS

32       N       (input) INTEGER
33               The order of the elementary reflector.
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35       ALPHA   (input/output) COMPLEX*16
36               On entry, the value alpha.  On exit, it is overwritten with the
37               value beta.
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39       X       (input/output) COMPLEX*16 array, dimension
40               (1+(N-2)*abs(INCX)) On entry, the vector x.   On  exit,  it  is
41               overwritten with the vector v.
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43       INCX    (input) INTEGER
44               The increment between elements of X. INCX > 0.
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46       TAU     (output) COMPLEX*16
47               The value tau.
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51 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       ZLARFG(1)