/*  -- translated by f2c (version 20100827).
   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 igraphdlarrk_(integer *n, integer *iw, doublereal *gl, 
	doublereal *gu, doublereal *d__, doublereal *e2, doublereal *pivmin, 
	doublereal *reltol, doublereal *w, doublereal *werr, integer *info)
{
    /* System generated locals */
    integer i__1;
    doublereal d__1, d__2;

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

    /* Local variables */
    integer i__, it;
    doublereal mid, eps, tmp1, tmp2, left, atoli, right;
    integer itmax;
    doublereal rtoli, tnorm;
    extern doublereal igraphdlamch_(char *);
    integer negcnt;


/*  -- LAPACK auxiliary routine (version 3.2) --   
    -- LAPACK is a software package provided by Univ. of Tennessee,    --   
    -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--   
       November 2006   


    Purpose   
    =======   

    DLARRK computes one eigenvalue of a symmetric tridiagonal   
    matrix T to suitable accuracy. This is an auxiliary code to be   
    called from DSTEMR.   

    To avoid overflow, the matrix must be scaled so that its   
    largest element is no greater than overflow**(1/2) *   
    underflow**(1/4) in absolute value, and for greatest   
    accuracy, it should not be much smaller than that.   

    See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal   
    Matrix", Report CS41, Computer Science Dept., Stanford   
    University, July 21, 1966.   

    Arguments   
    =========   

    N       (input) INTEGER   
            The order of the tridiagonal matrix T.  N >= 0.   

    IW      (input) INTEGER   
            The index of the eigenvalues to be returned.   

    GL      (input) DOUBLE PRECISION   
    GU      (input) DOUBLE PRECISION   
            An upper and a lower bound on the eigenvalue.   

    D       (input) DOUBLE PRECISION array, dimension (N)   
            The n diagonal elements of the tridiagonal matrix T.   

    E2      (input) DOUBLE PRECISION array, dimension (N-1)   
            The (n-1) squared off-diagonal elements of the tridiagonal matrix T.   

    PIVMIN  (input) DOUBLE PRECISION   
            The minimum pivot allowed in the Sturm sequence for T.   

    RELTOL  (input) DOUBLE PRECISION   
            The minimum relative width of an interval.  When an interval   
            is narrower than RELTOL times the larger (in   
            magnitude) endpoint, then it is considered to be   
            sufficiently small, i.e., converged.  Note: this should   
            always be at least radix*machine epsilon.   

    W       (output) DOUBLE PRECISION   

    WERR    (output) DOUBLE PRECISION   
            The error bound on the corresponding eigenvalue approximation   
            in W.   

    INFO    (output) INTEGER   
            = 0:       Eigenvalue converged   
            = -1:      Eigenvalue did NOT converge   

    Internal Parameters   
    ===================   

    FUDGE   DOUBLE PRECISION, default = 2   
            A "fudge factor" to widen the Gershgorin intervals.   

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


       Get machine constants   
       Parameter adjustments */
    --e2;
    --d__;

    /* Function Body */
    eps = igraphdlamch_("P");
/* Computing MAX */
    d__1 = abs(*gl), d__2 = abs(*gu);
    tnorm = max(d__1,d__2);
    rtoli = *reltol;
    atoli = *pivmin * 4.;
    itmax = (integer) ((log(tnorm + *pivmin) - log(*pivmin)) / log(2.)) + 2;
    *info = -1;
    left = *gl - tnorm * 2. * eps * *n - *pivmin * 4.;
    right = *gu + tnorm * 2. * eps * *n + *pivmin * 4.;
    it = 0;
L10:

/*     Check if interval converged or maximum number of iterations reached */

    tmp1 = (d__1 = right - left, abs(d__1));
/* Computing MAX */
    d__1 = abs(right), d__2 = abs(left);
    tmp2 = max(d__1,d__2);
/* Computing MAX */
    d__1 = max(atoli,*pivmin), d__2 = rtoli * tmp2;
    if (tmp1 < max(d__1,d__2)) {
	*info = 0;
	goto L30;
    }
    if (it > itmax) {
	goto L30;
    }

/*     Count number of negative pivots for mid-point */

    ++it;
    mid = (left + right) * .5;
    negcnt = 0;
    tmp1 = d__[1] - mid;
    if (abs(tmp1) < *pivmin) {
	tmp1 = -(*pivmin);
    }
    if (tmp1 <= 0.) {
	++negcnt;
    }

    i__1 = *n;
    for (i__ = 2; i__ <= i__1; ++i__) {
	tmp1 = d__[i__] - e2[i__ - 1] / tmp1 - mid;
	if (abs(tmp1) < *pivmin) {
	    tmp1 = -(*pivmin);
	}
	if (tmp1 <= 0.) {
	    ++negcnt;
	}
/* L20: */
    }
    if (negcnt >= *iw) {
	right = mid;
    } else {
	left = mid;
    }
    goto L10;
L30:

/*     Converged or maximum number of iterations reached */

    *w = (left + right) * .5;
    *werr = (d__1 = right - left, abs(d__1)) * .5;
    return 0;

/*     End of DLARRK */

} /* igraphdlarrk_ */

