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*/
#include "f2c.h"
/* > \brief \b DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
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> \endhtmlonly
Definition:
===========
SUBROUTINE DLARRK( N, IW, GL, GU,
D, E2, PIVMIN, RELTOL, W, WERR, INFO)
INTEGER INFO, IW, N
DOUBLE PRECISION PIVMIN, RELTOL, GL, GU, W, WERR
DOUBLE PRECISION D( * ), E2( * )
> \par Purpose:
=============
>
> \verbatim
>
> 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.
> \endverbatim
Arguments:
==========
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the tridiagonal matrix T. N >= 0.
> \endverbatim
>
> \param[in] IW
> \verbatim
> IW is INTEGER
> The index of the eigenvalues to be returned.
> \endverbatim
>
> \param[in] GL
> \verbatim
> GL is DOUBLE PRECISION
> \endverbatim
>
> \param[in] GU
> \verbatim
> GU is DOUBLE PRECISION
> An upper and a lower bound on the eigenvalue.
> \endverbatim
>
> \param[in] D
> \verbatim
> D is DOUBLE PRECISION array, dimension (N)
> The n diagonal elements of the tridiagonal matrix T.
> \endverbatim
>
> \param[in] E2
> \verbatim
> E2 is DOUBLE PRECISION array, dimension (N-1)
> The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
> \endverbatim
>
> \param[in] PIVMIN
> \verbatim
> PIVMIN is DOUBLE PRECISION
> The minimum pivot allowed in the Sturm sequence for T.
> \endverbatim
>
> \param[in] RELTOL
> \verbatim
> RELTOL is 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.
> \endverbatim
>
> \param[out] W
> \verbatim
> W is DOUBLE PRECISION
> \endverbatim
>
> \param[out] WERR
> \verbatim
> WERR is DOUBLE PRECISION
> The error bound on the corresponding eigenvalue approximation
> in W.
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0: Eigenvalue converged
> = -1: Eigenvalue did NOT converge
> \endverbatim
> \par Internal Parameters:
=========================
>
> \verbatim
> FUDGE DOUBLE PRECISION, default = 2
> A "fudge factor" to widen the Gershgorin intervals.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup auxOTHERauxiliary
=====================================================================
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 3.4.2) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
September 2012
=====================================================================
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_ */