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

6       ZLARFG  - a complex elementary reflector H of order n, such that   H' *
7       ( 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  )
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22       where alpha and  beta  are  scalars,  with  beta  real,  and  x  is  an
23       (n-1)-element complex vector. H is represented in the form
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25             H = I - tau * ( 1 ) * ( 1 v' ) ,
26                           ( v )
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28       where  tau is a complex scalar and v is a complex (n-1)-element vector.
29       Note that H is not hermitian.
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31       If the elements of x are all zero and alpha is real, then tau = 0 and H
32       is taken to be the unit matrix.
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34       Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .
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ARGUMENTS

38       N       (input) INTEGER
39               The order of the elementary reflector.
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41       ALPHA   (input/output) COMPLEX*16
42               On entry, the value alpha.  On exit, it is overwritten with the
43               value beta.
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45       X       (input/output) COMPLEX*16 array, dimension
46               (1+(N-2)*abs(INCX)) On entry, the vector x.   On  exit,  it  is
47               overwritten with the vector v.
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49       INCX    (input) INTEGER
50               The increment between elements of X. INCX > 0.
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52       TAU     (output) COMPLEX*16
53               The value tau.
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57 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       ZLARFG(1)