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NAME DLARFG - generate a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H' * H = I SYNOPSIS SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) INTEGER INCX, N DOUBLE PRECISION ALPHA, TAU DOUBLE PRECISION X( * ) PURPOSE DLARFG generates a real elementary reflector H of order n, such that ( x ) ( 0 ) where alpha and beta are scalars, and x is an (n-1)-element real vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v' ) , ( v ) where tau is a real scalar and v is a real (n-1)-element vector. If the elements of x are all zero, then tau = 0 and H is taken to be the unit matrix. Otherwise 1 <= tau <= 2. ARGUMENTS N (input) INTEGER The order of the elementary reflector. ALPHA (input/output) DOUBLE PRECISION On entry, the value alpha. On exit, it is overwrit- ten with the value beta. X (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION The value tau.