slarfg.c

来自「NIST Handwriting OCR Testbed」· C语言 代码 · 共 161 行

/*
* ======================================================================
* NIST Guide to Available Math Software.
* Fullsource for module SSYEVX.C from package CLAPACK.
* Retrieved from NETLIB on Fri Mar 10 14:23:44 2000.
* ======================================================================
*/
#include <f2c.h>

/* Subroutine */ int slarfg_(integer *n, real *alpha, real *x, integer *incx, 
	real *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   
    =======   

    SLARFG 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) 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.   

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


    
   Parameter adjustments   
       Function Body */
    /* System generated locals */
    integer i__1;
    real r__1;
    /* Builtin functions */
    double r_sign(real *, real *);
    /* Local variables */
    static real beta;
    extern doublereal snrm2_(integer *, real *, integer *);
    static integer j;
    extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *);
    static real xnorm;
    extern doublereal slapy2_(real *, real *), slamch_(char *);
    static real safmin, rsafmn;
    static integer knt;


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


    if (*n <= 1) {
	*tau = 0.f;
	return 0;
    }

    i__1 = *n - 1;
    xnorm = snrm2_(&i__1, &X(1), incx);

    if (xnorm == 0.f) {

/*        H  =  I */

	*tau = 0.f;
    } else {

/*        general case */

	r__1 = slapy2_(alpha, &xnorm);
	beta = -(doublereal)r_sign(&r__1, alpha);
	safmin = slamch_("S") / slamch_("E");
	if (dabs(beta) < safmin) {

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

	    rsafmn = 1.f / safmin;
	    knt = 0;
L10:
	    ++knt;
	    i__1 = *n - 1;
	    sscal_(&i__1, &rsafmn, &X(1), incx);
	    beta *= rsafmn;
	    *alpha *= rsafmn;
	    if (dabs(beta) < safmin) {
		goto L10;
	    }

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

	    i__1 = *n - 1;
	    xnorm = snrm2_(&i__1, &X(1), incx);
	    r__1 = slapy2_(alpha, &xnorm);
	    beta = -(doublereal)r_sign(&r__1, alpha);
	    *tau = (beta - *alpha) / beta;
	    i__1 = *n - 1;
	    r__1 = 1.f / (*alpha - beta);
	    sscal_(&i__1, &r__1, &X(1), incx);

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

	    *alpha = beta;
	    i__1 = knt;
	    for (j = 1; j <= knt; ++j) {
		*alpha *= safmin;
/* L20: */
	    }
	} else {
	    *tau = (beta - *alpha) / beta;
	    i__1 = *n - 1;
	    r__1 = 1.f / (*alpha - beta);
	    sscal_(&i__1, &r__1, &X(1), incx);
	    *alpha = beta;
	}
    }

    return 0;

/*     End of SLARFG */

} /* slarfg_ */