/* -- translated by f2c (version 20100827).
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*/
#include "f2c.h"
/* > \brief \b DLARRR performs tests to decide whether the symmetric tridiagonal matrix T warrants expensive c
omputations which guarantee high relative accuracy in the eigenvalues.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DLARRR + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrr.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrr.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrr.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DLARRR( N, D, E, INFO )
INTEGER N, INFO
DOUBLE PRECISION D( * ), E( * )
> \par Purpose:
=============
>
> \verbatim
>
> Perform tests to decide whether the symmetric tridiagonal matrix T
> warrants expensive computations which guarantee high relative accuracy
> in the eigenvalues.
> \endverbatim
Arguments:
==========
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix. N > 0.
> \endverbatim
>
> \param[in] D
> \verbatim
> D is DOUBLE PRECISION array, dimension (N)
> The N diagonal elements of the tridiagonal matrix T.
> \endverbatim
>
> \param[in,out] E
> \verbatim
> E is DOUBLE PRECISION array, dimension (N)
> On entry, the first (N-1) entries contain the subdiagonal
> elements of the tridiagonal matrix T; E(N) is set to ZERO.
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> INFO = 0(default) : the matrix warrants computations preserving
> relative accuracy.
> INFO = 1 : the matrix warrants computations guaranteeing
> only absolute accuracy.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date September 2012
> \ingroup auxOTHERauxiliary
> \par Contributors:
==================
>
> Beresford Parlett, University of California, Berkeley, USA \n
> Jim Demmel, University of California, Berkeley, USA \n
> Inderjit Dhillon, University of Texas, Austin, USA \n
> Osni Marques, LBNL/NERSC, USA \n
> Christof Voemel, University of California, Berkeley, USA
=====================================================================
Subroutine */ int igraphdlarrr_(integer *n, doublereal *d__, doublereal *e,
integer *info)
{
/* System generated locals */
integer i__1;
doublereal d__1;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__;
doublereal eps, tmp, tmp2, rmin;
extern doublereal igraphdlamch_(char *);
doublereal offdig, safmin;
logical yesrel;
doublereal smlnum, offdig2;
/* -- 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
=====================================================================
As a default, do NOT go for relative-accuracy preserving computations.
Parameter adjustments */
--e;
--d__;
/* Function Body */
*info = 1;
safmin = igraphdlamch_("Safe minimum");
eps = igraphdlamch_("Precision");
smlnum = safmin / eps;
rmin = sqrt(smlnum);
/* Tests for relative accuracy
Test for scaled diagonal dominance
Scale the diagonal entries to one and check whether the sum of the
off-diagonals is less than one
The sdd relative error bounds have a 1/(1- 2*x) factor in them,
x = max(OFFDIG + OFFDIG2), so when x is close to 1/2, no relative
accuracy is promised. In the notation of the code fragment below,
1/(1 - (OFFDIG + OFFDIG2)) is the condition number.
We don't think it is worth going into "sdd mode" unless the relative
condition number is reasonable, not 1/macheps.
The threshold should be compatible with other thresholds used in the
code. We set OFFDIG + OFFDIG2 <= .999 =: RELCOND, it corresponds
to losing at most 3 decimal digits: 1 / (1 - (OFFDIG + OFFDIG2)) <= 1000
instead of the current OFFDIG + OFFDIG2 < 1 */
yesrel = TRUE_;
offdig = 0.;
tmp = sqrt((abs(d__[1])));
if (tmp < rmin) {
yesrel = FALSE_;
}
if (! yesrel) {
goto L11;
}
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
tmp2 = sqrt((d__1 = d__[i__], abs(d__1)));
if (tmp2 < rmin) {
yesrel = FALSE_;
}
if (! yesrel) {
goto L11;
}
offdig2 = (d__1 = e[i__ - 1], abs(d__1)) / (tmp * tmp2);
if (offdig + offdig2 >= .999) {
yesrel = FALSE_;
}
if (! yesrel) {
goto L11;
}
tmp = tmp2;
offdig = offdig2;
/* L10: */
}
L11:
if (yesrel) {
*info = 0;
return 0;
} else {
}
/* *** MORE TO BE IMPLEMENTED ***
Test if the lower bidiagonal matrix L from T = L D L^T
(zero shift facto) is well conditioned
Test if the upper bidiagonal matrix U from T = U D U^T
(zero shift facto) is well conditioned.
In this case, the matrix needs to be flipped and, at the end
of the eigenvector computation, the flip needs to be applied
to the computed eigenvectors (and the support) */
return 0;
/* END OF DLARRR */
} /* igraphdlarrr_ */