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*/
#include "f2c.h"
/* > \brief \b DLARRA computes the splitting points with the specified threshold.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DLARRA + dependencies
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f">
> [TGZ]</a>
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> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarra.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DLARRA( N, D, E, E2, SPLTOL, TNRM,
NSPLIT, ISPLIT, INFO )
INTEGER INFO, N, NSPLIT
DOUBLE PRECISION SPLTOL, TNRM
INTEGER ISPLIT( * )
DOUBLE PRECISION D( * ), E( * ), E2( * )
> \par Purpose:
=============
>
> \verbatim
>
> Compute the splitting points with threshold SPLTOL.
> DLARRA sets any "small" off-diagonal elements to zero.
> \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)
> On entry, 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) need not be set.
> On exit, the entries E( ISPLIT( I ) ), 1 <= I <= NSPLIT,
> are set to zero, the other entries of E are untouched.
> \endverbatim
>
> \param[in,out] E2
> \verbatim
> E2 is DOUBLE PRECISION array, dimension (N)
> On entry, the first (N-1) entries contain the SQUARES of the
> subdiagonal elements of the tridiagonal matrix T;
> E2(N) need not be set.
> On exit, the entries E2( ISPLIT( I ) ),
> 1 <= I <= NSPLIT, have been set to zero
> \endverbatim
>
> \param[in] SPLTOL
> \verbatim
> SPLTOL is DOUBLE PRECISION
> The threshold for splitting. Two criteria can be used:
> SPLTOL<0 : criterion based on absolute off-diagonal value
> SPLTOL>0 : criterion that preserves relative accuracy
> \endverbatim
>
> \param[in] TNRM
> \verbatim
> TNRM is DOUBLE PRECISION
> The norm of the matrix.
> \endverbatim
>
> \param[out] NSPLIT
> \verbatim
> NSPLIT is INTEGER
> The number of blocks T splits into. 1 <= NSPLIT <= N.
> \endverbatim
>
> \param[out] ISPLIT
> \verbatim
> ISPLIT is INTEGER array, dimension (N)
> The splitting points, at which T breaks up into blocks.
> The first block consists of rows/columns 1 to ISPLIT(1),
> the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
> etc., and the NSPLIT-th consists of rows/columns
> ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0: successful exit
> \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 igraphdlarra_(integer *n, doublereal *d__, doublereal *e,
doublereal *e2, doublereal *spltol, doublereal *tnrm, integer *nsplit,
integer *isplit, integer *info)
{
/* System generated locals */
integer i__1;
doublereal d__1, d__2;
/* Builtin functions */
double sqrt(doublereal);
/* Local variables */
integer i__;
doublereal tmp1, eabs;
/* -- 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
=====================================================================
Parameter adjustments */
--isplit;
--e2;
--e;
--d__;
/* Function Body */
*info = 0;
/* Compute splitting points */
*nsplit = 1;
if (*spltol < 0.) {
/* Criterion based on absolute off-diagonal value */
tmp1 = abs(*spltol) * *tnrm;
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
eabs = (d__1 = e[i__], abs(d__1));
if (eabs <= tmp1) {
e[i__] = 0.;
e2[i__] = 0.;
isplit[*nsplit] = i__;
++(*nsplit);
}
/* L9: */
}
} else {
/* Criterion that guarantees relative accuracy */
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
eabs = (d__1 = e[i__], abs(d__1));
if (eabs <= *spltol * sqrt((d__1 = d__[i__], abs(d__1))) * sqrt((
d__2 = d__[i__ + 1], abs(d__2)))) {
e[i__] = 0.;
e2[i__] = 0.;
isplit[*nsplit] = i__;
++(*nsplit);
}
/* L10: */
}
}
isplit[*nsplit] = *n;
return 0;
/* End of DLARRA */
} /* igraphdlarra_ */