Provided by: liblapack-doc_3.3.1-1_all

**NAME**

LAPACK-3 - generates a real elementary reflector H of order n, such that H * ( alpha ) = ( beta ), H**T * H = I

**SYNOPSIS**

SUBROUTINE SLARFGP( N, ALPHA, X, INCX, TAU ) INTEGER INCX, N REAL ALPHA, TAU REAL X( * )

**PURPOSE**

SLARFGP generates a real elementary reflector H of order n, such that ( x ) ( 0 ) where alpha and beta are scalars, beta is non-negative, and x is an (n-1)-element real vector. H is represented in the form H = I - tau * ( 1 ) * ( 1 v**T ) , ( 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.

**ARGUMENTS**

N (input) INTEGER The order of the elementary reflector. ALPHA (input/output) REAL On entry, the value alpha. On exit, it is overwritten with the value beta. X (input/output) REAL 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) REAL The value tau. LAPACK auxiliary routine (version 3.3.1) April 2011 SLARFGP(3lapack)