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references/igraph-1.0.1/vendor/lapack/dlarrc.c
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/* -- translated by f2c (version 20240504).
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"
/* > \brief \b DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DLARRC + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrc.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrc.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrc.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
EIGCNT, LCNT, RCNT, INFO )
CHARACTER JOBT
INTEGER EIGCNT, INFO, LCNT, N, RCNT
DOUBLE PRECISION PIVMIN, VL, VU
DOUBLE PRECISION D( * ), E( * )
> \par Purpose:
=============
>
> \verbatim
>
> Find the number of eigenvalues of the symmetric tridiagonal matrix T
> that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T
> if JOBT = 'L'.
> \endverbatim
Arguments:
==========
> \param[in] JOBT
> \verbatim
> JOBT is CHARACTER*1
> = 'T': Compute Sturm count for matrix T.
> = 'L': Compute Sturm count for matrix L D L^T.
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix. N > 0.
> \endverbatim
>
> \param[in] VL
> \verbatim
> VL is DOUBLE PRECISION
> \endverbatim
>
> \param[in] VU
> \verbatim
> VU is DOUBLE PRECISION
> The lower and upper bounds for the eigenvalues.
> \endverbatim
>
> \param[in] D
> \verbatim
> D is DOUBLE PRECISION array, dimension (N)
> JOBT = 'T': The N diagonal elements of the tridiagonal matrix T.
> JOBT = 'L': The N diagonal elements of the diagonal matrix D.
> \endverbatim
>
> \param[in] E
> \verbatim
> E is DOUBLE PRECISION array, dimension (N)
> JOBT = 'T': The N-1 offdiagonal elements of the matrix T.
> JOBT = 'L': The N-1 offdiagonal elements of the matrix L.
> \endverbatim
>
> \param[in] PIVMIN
> \verbatim
> PIVMIN is DOUBLE PRECISION
> The minimum pivot in the Sturm sequence for T.
> \endverbatim
>
> \param[out] EIGCNT
> \verbatim
> EIGCNT is INTEGER
> The number of eigenvalues of the symmetric tridiagonal matrix T
> that are in the interval (VL,VU]
> \endverbatim
>
> \param[out] LCNT
> \verbatim
> LCNT is INTEGER
> \endverbatim
>
> \param[out] RCNT
> \verbatim
> RCNT is INTEGER
> The left and right negcounts of the interval.
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> \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 igraphdlarrc_(char *jobt, integer *n, doublereal *vl,
doublereal *vu, doublereal *d__, doublereal *e, doublereal *pivmin,
integer *eigcnt, integer *lcnt, integer *rcnt, integer *info)
{
/* System generated locals */
integer i__1;
doublereal d__1;
/* Local variables */
integer i__;
doublereal sl, su, tmp, tmp2;
logical matt;
extern logical igraphlsame_(char *, char *);
doublereal lpivot, rpivot;
/* -- 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 */
--e;
--d__;
/* Function Body */
*info = 0;
*lcnt = 0;
*rcnt = 0;
*eigcnt = 0;
matt = igraphlsame_(jobt, "T");
if (matt) {
/* Sturm sequence count on T */
lpivot = d__[1] - *vl;
rpivot = d__[1] - *vu;
if (lpivot <= 0.) {
++(*lcnt);
}
if (rpivot <= 0.) {
++(*rcnt);
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing 2nd power */
d__1 = e[i__];
tmp = d__1 * d__1;
lpivot = d__[i__ + 1] - *vl - tmp / lpivot;
rpivot = d__[i__ + 1] - *vu - tmp / rpivot;
if (lpivot <= 0.) {
++(*lcnt);
}
if (rpivot <= 0.) {
++(*rcnt);
}
/* L10: */
}
} else {
/* Sturm sequence count on L D L^T */
sl = -(*vl);
su = -(*vu);
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
lpivot = d__[i__] + sl;
rpivot = d__[i__] + su;
if (lpivot <= 0.) {
++(*lcnt);
}
if (rpivot <= 0.) {
++(*rcnt);
}
tmp = e[i__] * d__[i__] * e[i__];
tmp2 = tmp / lpivot;
if (tmp2 == 0.) {
sl = tmp - *vl;
} else {
sl = sl * tmp2 - *vl;
}
tmp2 = tmp / rpivot;
if (tmp2 == 0.) {
su = tmp - *vu;
} else {
su = su * tmp2 - *vu;
}
/* L20: */
}
lpivot = d__[*n] + sl;
rpivot = d__[*n] + su;
if (lpivot <= 0.) {
++(*lcnt);
}
if (rpivot <= 0.) {
++(*rcnt);
}
}
*eigcnt = *rcnt - *lcnt;
return 0;
/* end of DLARRC */
} /* igraphdlarrc_ */