#include "blaswrap.h"
/* slaed5.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"

/* Subroutine */ int slaed5_(integer *i__, real *d__, real *z__, real *delta, 
	real *rho, real *dlam)
{
    /* System generated locals */
    real r__1;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    static real b, c__, w, del, tau, temp;


/*  -- LAPACK routine (version 3.1) --   
       Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..   
       November 2006   


    Purpose   
    =======   

    This subroutine computes the I-th eigenvalue of a symmetric rank-one   
    modification of a 2-by-2 diagonal matrix   

               diag( D )  +  RHO *  Z * transpose(Z) .   

    The diagonal elements in the array D are assumed to satisfy   

               D(i) < D(j)  for  i < j .   

    We also assume RHO > 0 and that the Euclidean norm of the vector   
    Z is one.   

    Arguments   
    =========   

    I      (input) INTEGER   
           The index of the eigenvalue to be computed.  I = 1 or I = 2.   

    D      (input) REAL array, dimension (2)   
           The original eigenvalues.  We assume D(1) < D(2).   

    Z      (input) REAL array, dimension (2)   
           The components of the updating vector.   

    DELTA  (output) REAL array, dimension (2)   
           The vector DELTA contains the information necessary   
           to construct the eigenvectors.   

    RHO    (input) REAL   
           The scalar in the symmetric updating formula.   

    DLAM   (output) REAL   
           The computed lambda_I, the I-th updated eigenvalue.   

    Further Details   
    ===============   

    Based on contributions by   
       Ren-Cang Li, Computer Science Division, University of California   
       at Berkeley, USA   

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


       Parameter adjustments */
    --delta;
    --z__;
    --d__;

    /* Function Body */
    del = d__[2] - d__[1];
    if (*i__ == 1) {
	w = *rho * 2.f * (z__[2] * z__[2] - z__[1] * z__[1]) / del + 1.f;
	if (w > 0.f) {
	    b = del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
	    c__ = *rho * z__[1] * z__[1] * del;

/*           B > ZERO, always */

	    tau = c__ * 2.f / (b + sqrt((r__1 = b * b - c__ * 4.f, dabs(r__1)) 		    ));
	    *dlam = d__[1] + tau;
	    delta[1] = -z__[1] / tau;
	    delta[2] = z__[2] / (del - tau);
	} else {
	    b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
	    c__ = *rho * z__[2] * z__[2] * del;
	    if (b > 0.f) {
		tau = c__ * -2.f / (b + sqrt(b * b + c__ * 4.f));
	    } else {
		tau = (b - sqrt(b * b + c__ * 4.f)) / 2.f;
	    }
	    *dlam = d__[2] + tau;
	    delta[1] = -z__[1] / (del + tau);
	    delta[2] = -z__[2] / tau;
	}
	temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]);
	delta[1] /= temp;
	delta[2] /= temp;
    } else {

/*     Now I=2 */

	b = -del + *rho * (z__[1] * z__[1] + z__[2] * z__[2]);
	c__ = *rho * z__[2] * z__[2] * del;
	if (b > 0.f) {
	    tau = (b + sqrt(b * b + c__ * 4.f)) / 2.f;
	} else {
	    tau = c__ * 2.f / (-b + sqrt(b * b + c__ * 4.f));
	}
	*dlam = d__[2] + tau;
	delta[1] = -z__[1] / (del + tau);
	delta[2] = -z__[2] / tau;
	temp = sqrt(delta[1] * delta[1] + delta[2] * delta[2]);
	delta[1] /= temp;
	delta[2] /= temp;
    }
    return 0;

/*     End OF SLAED5 */

} /* slaed5_ */