.TH ZLARFG 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME ZLARFG - a complex elementary reflector H of order n, such that H\(aq * ( alpha ) = ( beta ), H\(aq * H = I .SH SYNOPSIS .TP 19 SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU ) .TP 19 .ti +4 INTEGER INCX, N .TP 19 .ti +4 COMPLEX*16 ALPHA, TAU .TP 19 .ti +4 COMPLEX*16 X( * ) .SH PURPOSE ZLARFG generates a complex elementary reflector H of order n, such that ( x ) ( 0 ) .br 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\(aq ) , .br ( v ) .br where tau is a complex scalar and v is a complex (n-1)-element vector. Note that H is not hermitian. .br If the elements of x are all zero and alpha is real, then tau = 0 and H is taken to be the unit matrix. .br Otherwise 1 <= real(tau) <= 2 and abs(tau-1) <= 1 . .br .SH ARGUMENTS .TP 8 N (input) INTEGER The order of the elementary reflector. .TP 8 ALPHA (input/output) COMPLEX*16 On entry, the value alpha. On exit, it is overwritten with the value beta. .TP 8 X (input/output) COMPLEX*16 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) COMPLEX*16 The value tau.