zlarfg.c

来自「算断裂的」· C语言 代码 · 共 183 行

#include "f2c.h"

/* Subroutine */ int zlarfg_(integer *n, doublecomplex *alpha, doublecomplex *
	x, integer *incx, doublecomplex *tau)
{
/*  -- LAPACK auxiliary routine (version 2.0) --   
       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   
       Function Body */
    /* 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;



#define X(I) x[(I)-1]


    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 <= knt; ++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_ */