Function dlarfg_

numpy/linalg/lapack_lite/f2c_d_lapack.c:22337–22476

Subroutine */

} /* dlarfb_ */

/* Subroutine */ int dlarfg_(integer *n, doublereal *alpha, doublereal *x,
	integer *incx, doublereal *tau)
{
    /* System generated locals */
    integer i__1;
    doublereal d__1;

    /* Local variables */
    static integer j, knt;
    static doublereal beta;
    extern doublereal dnrm2_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
	    integer *);
    static doublereal xnorm;

    static doublereal safmin, rsafmn;


/*
    -- LAPACK auxiliary routine (version 3.2) --
    -- LAPACK is a software package provided by Univ. of Tennessee,    --
    -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
       November 2006


    Purpose
    =======

    DLARFG generates a real elementary reflector H of order n, such
    that

          H * ( alpha ) = ( beta ),   H' * H = I.
              (   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 overwritten with the value beta.