Beispiel #1
0
/* Subroutine */ int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex *
	x, integer *incx, doublecomplex *tau)
{
/*  -- LAPACK auxiliary routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       September 30, 1994   


    Purpose   
    =======   

    ZLARFG 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, with beta real, 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.   

    =====================================================================   


       Parameter adjustments */
    /* Table of constant values */
    static doublecomplex c_b5 = {1.,0.};
    
    /* System generated locals */
    integer i__1;
    doublereal d__1, d__2;
    doublecomplex z__1, z__2;
    /* Builtin functions */
    double d_imag(doublecomplex *), d_sign(doublereal *, doublereal *);
    /* Local variables */
    static doublereal beta;
    static integer j;
    static doublereal alphi, alphr;
    extern /* Subroutine */ int zscal_(integer *, doublecomplex *, 
	    doublecomplex *, integer *);
    static doublereal xnorm;
    extern doublereal dlapy3_(doublereal *, doublereal *, doublereal *), 
	    dznrm2_(integer *, doublecomplex *, integer *), dlamch_(char *);
    static doublereal safmin;
    extern /* Subroutine */ int zdscal_(integer *, doublereal *, 
	    doublecomplex *, integer *);
    static doublereal rsafmn;
    extern /* Double Complex */ VOID zladiv_(doublecomplex *, doublecomplex *,
	     doublecomplex *);
    static integer knt;


    --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  =  I */

	tau->r = 0., tau->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;

	if (abs(beta) < safmin) {

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

	    knt = 0;
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);
	    d__1 = (beta - 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;
	    z__2.r = alpha->r - beta, z__2.i = alpha->i;
	    zladiv_(&z__1, &c_b5, &z__2);
	    alpha->r = z__1.r, alpha->i = z__1.i;
	    i__1 = *n - 1;
	    zscal_(&i__1, alpha, &x[1], incx);

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

	    alpha->r = beta, alpha->i = 0.;
	    i__1 = knt;
	    for (j = 1; j <= i__1; ++j) {
		z__1.r = safmin * alpha->r, z__1.i = safmin * alpha->i;
		alpha->r = z__1.r, alpha->i = z__1.i;
/* L20: */
	    }
	} else {
	    d__1 = (beta - 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;
	    z__2.r = alpha->r - beta, z__2.i = alpha->i;
	    zladiv_(&z__1, &c_b5, &z__2);
	    alpha->r = z__1.r, alpha->i = z__1.i;
	    i__1 = *n - 1;
	    zscal_(&i__1, alpha, &x[1], incx);
	    alpha->r = beta, alpha->i = 0.;
	}
    }

    return 0;

/*     End of ZLARFG */

} /* zlarfg_ */
Beispiel #2
0
/* Subroutine */
int zlarfgp_(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 *), z_abs( doublecomplex *);
    /* Local variables */
    integer j;
    doublecomplex savealpha;
    integer 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 *);
    extern /* Subroutine */
    int zdscal_(integer *, doublereal *, doublecomplex *, integer *);
    doublereal bignum;
    extern /* Double Complex */
    VOID zladiv_(doublecomplex *, doublecomplex *, doublecomplex *);
    doublereal smlnum;
    /* -- LAPACK auxiliary routine (version 3.4.2) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* September 2012 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. 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.)
    {
        /* 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.; // , expr subst
                }
                z__1.r = -alpha->r;
                z__1.i = -alpha->i; // , expr subst
                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; // , expr subst
            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.; // , expr subst
            }
            alpha->r = xnorm, alpha->i = 0.;
        }
    }
    else
    {
        /* general case */
        d__1 = dlapy3_(&alphr, &alphi, &xnorm);
        beta = d_sign(&d__1, &alphr);
        smlnum = dlamch_("S") / dlamch_("E");
        bignum = 1. / smlnum;
        knt = 0;
        if (abs(beta) < smlnum)
        {
            /* XNORM, BETA may be inaccurate;
            scale X and recompute them */
L10:
            ++knt;
            i__1 = *n - 1;
            zdscal_(&i__1, &bignum, &x[1], incx);
            beta *= bignum;
            alphi *= bignum;
            alphr *= bignum;
            if (abs(beta) < smlnum)
            {
                goto L10;
            }
            /* New BETA is at most 1, at least SMLNUM */
            i__1 = *n - 1;
            xnorm = dznrm2_(&i__1, &x[1], incx);
            z__1.r = alphr;
            z__1.i = alphi; // , expr subst
            alpha->r = z__1.r, alpha->i = z__1.i;
            d__1 = dlapy3_(&alphr, &alphi, &xnorm);
            beta = d_sign(&d__1, &alphr);
        }
        savealpha.r = alpha->r;
        savealpha.i = alpha->i; // , expr subst
        z__1.r = alpha->r + beta;
        z__1.i = alpha->i; // , expr subst
        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; // , expr subst
            z__1.r = z__2.r / beta;
            z__1.i = z__2.i / beta; // , expr subst
            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; // , expr subst
            tau->r = z__1.r, tau->i = z__1.i;
            d__1 = -alphr;
            z__1.r = d__1;
            z__1.i = alphi; // , expr subst
            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;
        if (z_abs(tau) <= smlnum)
        {
            /* In the case where the computed TAU ends up being a denormalized number, */
            /* it loses relative accuracy. This is a BIG problem. Solution: flush TAU */
            /* to ZERO (or TWO or whatever makes a nonnegative real number for BETA). */
            /* (Bug report provided by Pat Quillen from MathWorks on Jul 29, 2009.) */
            /* (Thanks Pat. Thanks MathWorks.) */
            alphr = savealpha.r;
            alphi = d_imag(&savealpha);
            if (alphi == 0.)
            {
                if (alphr >= 0.)
                {
                    tau->r = 0., tau->i = 0.;
                }
                else
                {
                    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.; // , expr subst
                    }
                    z__1.r = -savealpha.r;
                    z__1.i = -savealpha.i; // , expr subst
                    beta = z__1.r;
                }
            }
            else
            {
                xnorm = dlapy2_(&alphr, &alphi);
                d__1 = 1. - alphr / xnorm;
                d__2 = -alphi / xnorm;
                z__1.r = d__1;
                z__1.i = d__2; // , expr subst
                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.; // , expr subst
                }
                beta = xnorm;
            }
        }
        else
        {
            /* This is the general case. */
            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 *= smlnum;
            /* L20: */
        }
        alpha->r = beta, alpha->i = 0.;
    }
    return 0;
    /* End of ZLARFGP */
}
Beispiel #3
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_ */