zlarfp.c

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/* zlarfp.f -- translated by f2c (version 20061008).
   You must link the resulting object file with libf2c:
        on Microsoft Windows system, link with libf2c.lib;
        on Linux or Unix systems, link with .../path/to/libf2c.a -lm
        or, if you install libf2c.a in a standard place, with -lf2c -lm
        -- in that order, at the end of the command line, as in
                cc *.o -lf2c -lm
        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

                http://www.netlib.org/f2c/libf2c.zip
*/

#include "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static doublecomplex c_b5 = {1.,0.};

/* Subroutine */ int zlarfp_(integer *n, doublecomplex *alpha, doublecomplex *
        x, integer *incx, doublecomplex *tau)
{
    /* System generated locals */
    integer i__1, i__2;
    doublereal d__1, d__2;
    doublecomplex z__1, z__2;

    /* Builtin functions */
    double d_imag(doublecomplex *), d_sign(doublereal *, doublereal *);

    /* Local variables */
    integer j, knt;
    doublereal beta, alphi, alphr;
    extern /* Subroutine */ int zscal_(integer *, doublecomplex *, 
            doublecomplex *, integer *);
    doublereal xnorm;
    extern doublereal dlapy2_(doublereal *, doublereal *), dlapy3_(doublereal 
            *, doublereal *, doublereal *), dznrm2_(integer *, doublecomplex *
, integer *), dlamch_(char *);
    doublereal safmin;
    extern /* Subroutine */ int zdscal_(integer *, doublereal *, 
            doublecomplex *, integer *);
    doublereal rsafmn;
    extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *, 
             doublecomplex *);


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  ZLARFP generates a complex elementary reflector H of order n, such */
/*  that */

/*        H' * ( alpha ) = ( beta ),   H' * H = I. */
/*             (   x   )   (   0  ) */

/*  where alpha and beta are scalars, beta is real and non-negative, and */
/*  x is an (n-1)-element complex vector.  H is represented in the form */

/*        H = I - tau * ( 1 ) * ( 1 v' ) , */
/*                      ( v ) */

/*  where tau is a complex scalar and v is a complex (n-1)-element */
/*  vector. Note that H is not hermitian. */

/*  If the elements of x are all zero and alpha is real, then tau = 0 */
/*  and H is taken to be the unit matrix. */

/*  Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 . */

/*  Arguments */
/*  ========= */

/*  N       (input) INTEGER */
/*          The order of the elementary reflector. */

/*  ALPHA   (input/output) COMPLEX*16 */
/*          On entry, the value alpha. */
/*          On exit, it is overwritten with the value beta. */

/*  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. */

/*  INCX    (input) INTEGER */
/*          The increment between elements of X. INCX > 0. */

/*  TAU     (output) COMPLEX*16 */
/*          The value tau. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Executable Statements .. */

    /* Parameter adjustments */
    --x;

    /* Function Body */
    if (*n <= 0) {
        tau->r = 0., tau->i = 0.;
        return 0;
    }

    i__1 = *n - 1;
    xnorm = dznrm2_(&i__1, &x[1], incx);
    alphr = alpha->r;
    alphi = d_imag(alpha);

    if (xnorm == 0. && alphi == 0.) {

/*        H  =  [1-alpha/abs(alpha) 0; 0 I], sign chosen so ALPHA >= 0. */

        if (alphi == 0.) {
            if (alphr >= 0.) {
/*              When TAU.eq.ZERO, the vector is special-cased to be */
/*              all zeros in the application routines.  We do not need */
/*              to clear it. */
                tau->r = 0., tau->i = 0.;
            } else {
/*              However, the application routines rely on explicit */
/*              zero checks when TAU.ne.ZERO, and we must clear X. */
                tau->r = 2., tau->i = 0.;
                i__1 = *n - 1;
                for (j = 1; j <= i__1; ++j) {
                    i__2 = (j - 1) * *incx + 1;
                    x[i__2].r = 0., x[i__2].i = 0.;
                }
                z__1.r = -alpha->r, z__1.i = -alpha->i;
                alpha->r = z__1.r, alpha->i = z__1.i;
            }
        } else {
/*           Only "reflecting" the diagonal entry to be real and non-negative. */
            xnorm = dlapy2_(&alphr, &alphi);
            d__1 = 1. - alphr / xnorm;
            d__2 = -alphi / xnorm;
            z__1.r = d__1, z__1.i = d__2;
            tau->r = z__1.r, tau->i = z__1.i;
            i__1 = *n - 1;
            for (j = 1; j <= i__1; ++j) {
                i__2 = (j - 1) * *incx + 1;
                x[i__2].r = 0., x[i__2].i = 0.;
            }
            alpha->r = xnorm, alpha->i = 0.;
        }
    } else {

/*        general case */

        d__1 = dlapy3_(&alphr, &alphi, &xnorm);
        beta = d_sign(&d__1, &alphr);
        safmin = dlamch_("S") / dlamch_("E");
        rsafmn = 1. / safmin;

        knt = 0;
        if (abs(beta) < safmin) {

/*           XNORM, BETA may be inaccurate; scale X and recompute them */

L10:
            ++knt;
            i__1 = *n - 1;
            zdscal_(&i__1, &rsafmn, &x[1], incx);
            beta *= rsafmn;
            alphi *= rsafmn;
            alphr *= rsafmn;
            if (abs(beta) < safmin) {
                goto L10;
            }

/*           New BETA is at most 1, at least SAFMIN */

            i__1 = *n - 1;
            xnorm = dznrm2_(&i__1, &x[1], incx);
            z__1.r = alphr, z__1.i = alphi;
            alpha->r = z__1.r, alpha->i = z__1.i;
            d__1 = dlapy3_(&alphr, &alphi, &xnorm);
            beta = d_sign(&d__1, &alphr);
        }
        z__1.r = alpha->r + beta, z__1.i = alpha->i;
        alpha->r = z__1.r, alpha->i = z__1.i;
        if (beta < 0.) {
            beta = -beta;
            z__2.r = -alpha->r, z__2.i = -alpha->i;
            z__1.r = z__2.r / beta, z__1.i = z__2.i / beta;
            tau->r = z__1.r, tau->i = z__1.i;
        } else {
            alphr = alphi * (alphi / alpha->r);
            alphr += xnorm * (xnorm / alpha->r);
            d__1 = alphr / beta;
            d__2 = -alphi / beta;
            z__1.r = d__1, z__1.i = d__2;
            tau->r = z__1.r, tau->i = z__1.i;
            d__1 = -alphr;
            z__1.r = d__1, z__1.i = alphi;
            alpha->r = z__1.r, alpha->i = z__1.i;
        }
        zladiv_(&z__1, &c_b5, alpha);
        alpha->r = z__1.r, alpha->i = z__1.i;
        i__1 = *n - 1;
        zscal_(&i__1, alpha, &x[1], incx);

/*        If BETA is subnormal, it may lose relative accuracy */

        i__1 = knt;
        for (j = 1; j <= i__1; ++j) {
            beta *= safmin;
/* L20: */
        }
        alpha->r = beta, alpha->i = 0.;
    }

    return 0;

/*     End of ZLARFP */

} /* zlarfp_ */