clarfg(3S)

NAME
     CLARFG - generate a complex elementary reflector H of order n, such that
     H' * ( alpha ) = ( beta ), H' * H = I

SYNOPSIS
     SUBROUTINE CLARFG( N, ALPHA, X, INCX, TAU )

         INTEGER        INCX, N

         COMPLEX        ALPHA, TAU

         COMPLEX        X( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     CLARFG generates a complex elementary reflector H of order n, such that
     H' * ( alpha ) = ( beta ), H' * H = I.            (   x   )   (   0  )

     where alpha and beta are scalars, with beta real, and x is an (n-1)-
     element complex vector. H is represented in the form

           H = I - tau * ( 1 ) * ( 1 v' ) ,
                         ( v )

     where tau is a complex scalar and v is a complex (n-1)-element vector.
     Note that H is not hermitian.

     If the elements of x are all zero and alpha is real, then tau = 0 and H
     is taken to be the unit matrix.

     Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .


ARGUMENTS
     N       (input) INTEGER
             The order of the elementary reflector.

     ALPHA   (input/output) COMPLEX
             On entry, the value alpha.  On exit, it is overwritten with the
             value beta.
     X       (input/output) COMPLEX array, dimension
             (1+(N-2)*abs(INCX)) On entry, the vector x.  On exit, it is
             overwritten with the vector v.

     INCX    (input) INTEGER
             The increment between elements of X. INCX > 0.

     TAU     (output) COMPLEX
             The value tau.

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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