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

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

10       SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
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12           INTEGER        INCX, N
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14           DOUBLE         PRECISION ALPHA, TAU
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16           DOUBLE         PRECISION X( * )
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PURPOSE

19       DLARFG generates a real elementary reflector H of order n, such that
20                 (   x   )   (   0  )
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22       where alpha and beta are scalars, and x is an (n-1)-element  real  vec‐
23       tor. 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 real scalar and v is a real (n-1)-element
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31       If  the  elements  of x are all zero, then tau = 0 and H is taken to be
32       the unit matrix.
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34       Otherwise  1 <= tau <= 2.
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ARGUMENTS

38       N       (input) INTEGER
39               The order of the elementary reflector.
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41       ALPHA   (input/output) DOUBLE PRECISION
42               On entry, the value alpha.  On exit, it is overwritten with the
43               value beta.
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45       X       (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION
53               The value tau.
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57 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       DLARFG(1)