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

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

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

19       SLARFG generates a real elementary reflector H of order n, such that
20                 (   x   )   (   0  )
21       where alpha and beta are scalars, and x is an (n-1)-element  real  vec‐
22       tor. H is represented in the form
23             H = I - tau * ( 1 ) * ( 1 v' ) ,
24                           ( v )
25       where tau is a real scalar and v is a real (n-1)-element
26       vector.
27       If  the  elements  of x are all zero, then tau = 0 and H is taken to be
28       the unit matrix.
29       Otherwise  1 <= tau <= 2.
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ARGUMENTS

32       N       (input) INTEGER
33               The order of the elementary reflector.
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35       ALPHA   (input/output) REAL
36               On entry, the value alpha.  On exit, it is overwritten with the
37               value beta.
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39       X       (input/output) REAL 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) REAL
47               The value tau.
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51 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLARFG(1)