.TH DLARFG 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME DLARFG - a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H\(aq * H = I .SH SYNOPSIS .TP 19 SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU ) .TP 19 .ti +4 INTEGER INCX, N .TP 19 .ti +4 DOUBLE PRECISION ALPHA, TAU .TP 19 .ti +4 DOUBLE PRECISION X( * ) .SH PURPOSE DLARFG generates a real elementary reflector H of order n, such that ( x ) ( 0 ) .br where alpha and beta are scalars, and x is an (n-1)-element real vector. H is represented in the form .br H = I - tau * ( 1 ) * ( 1 v\(aq ) , .br ( v ) .br where tau is a real scalar and v is a real (n-1)-element .br vector. .br If the elements of x are all zero, then tau = 0 and H is taken to be the unit matrix. .br Otherwise 1 <= tau <= 2. .br .SH ARGUMENTS .TP 8 N (input) INTEGER The order of the elementary reflector. .TP 8 ALPHA (input/output) DOUBLE PRECISION On entry, the value alpha. On exit, it is overwritten with the value beta. .TP 8 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. .TP 8 INCX (input) INTEGER The increment between elements of X. INCX > 0. .TP 8 TAU (output) DOUBLE PRECISION The value tau.