Abdelrahman Said
256 lines
6.7 KiB
C
256 lines
6.7 KiB
C
/* -- translated by f2c (version 20240504).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#include "f2c.h"
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/* > \brief \b DLARRC computes the number of eigenvalues of the symmetric tridiagonal matrix.
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=========== DOCUMENTATION ===========
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Online html documentation available at
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http://www.netlib.org/lapack/explore-html/
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> \htmlonly
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> Download DLARRC + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrc.
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f">
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> [TGZ]</a>
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrc.
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f">
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> [ZIP]</a>
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrc.
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f">
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> [TXT]</a>
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> \endhtmlonly
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Definition:
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===========
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SUBROUTINE DLARRC( JOBT, N, VL, VU, D, E, PIVMIN,
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EIGCNT, LCNT, RCNT, INFO )
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CHARACTER JOBT
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INTEGER EIGCNT, INFO, LCNT, N, RCNT
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DOUBLE PRECISION PIVMIN, VL, VU
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DOUBLE PRECISION D( * ), E( * )
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> \par Purpose:
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=============
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>
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> \verbatim
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>
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> Find the number of eigenvalues of the symmetric tridiagonal matrix T
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> that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T
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> if JOBT = 'L'.
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> \endverbatim
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Arguments:
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==========
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> \param[in] JOBT
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> \verbatim
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> JOBT is CHARACTER*1
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> = 'T': Compute Sturm count for matrix T.
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> = 'L': Compute Sturm count for matrix L D L^T.
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> \endverbatim
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>
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> \param[in] N
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> \verbatim
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> N is INTEGER
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> The order of the matrix. N > 0.
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> \endverbatim
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>
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> \param[in] VL
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> \verbatim
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> VL is DOUBLE PRECISION
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> \endverbatim
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>
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> \param[in] VU
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> \verbatim
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> VU is DOUBLE PRECISION
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> The lower and upper bounds for the eigenvalues.
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> \endverbatim
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>
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> \param[in] D
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> \verbatim
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> D is DOUBLE PRECISION array, dimension (N)
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> JOBT = 'T': The N diagonal elements of the tridiagonal matrix T.
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> JOBT = 'L': The N diagonal elements of the diagonal matrix D.
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> \endverbatim
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>
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> \param[in] E
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> \verbatim
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> E is DOUBLE PRECISION array, dimension (N)
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> JOBT = 'T': The N-1 offdiagonal elements of the matrix T.
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> JOBT = 'L': The N-1 offdiagonal elements of the matrix L.
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> \endverbatim
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>
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> \param[in] PIVMIN
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> \verbatim
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> PIVMIN is DOUBLE PRECISION
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> The minimum pivot in the Sturm sequence for T.
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> \endverbatim
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>
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> \param[out] EIGCNT
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> \verbatim
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> EIGCNT is INTEGER
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> The number of eigenvalues of the symmetric tridiagonal matrix T
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> that are in the interval (VL,VU]
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> \endverbatim
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>
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> \param[out] LCNT
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> \verbatim
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> LCNT is INTEGER
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> \endverbatim
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>
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> \param[out] RCNT
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> \verbatim
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> RCNT is INTEGER
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> The left and right negcounts of the interval.
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> \endverbatim
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>
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> \param[out] INFO
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> \verbatim
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> INFO is INTEGER
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> \endverbatim
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Authors:
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========
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> \author Univ. of Tennessee
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> \author Univ. of California Berkeley
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> \author Univ. of Colorado Denver
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> \author NAG Ltd.
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> \date September 2012
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> \ingroup auxOTHERauxiliary
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> \par Contributors:
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==================
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>
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> Beresford Parlett, University of California, Berkeley, USA \n
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> Jim Demmel, University of California, Berkeley, USA \n
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> Inderjit Dhillon, University of Texas, Austin, USA \n
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> Osni Marques, LBNL/NERSC, USA \n
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> Christof Voemel, University of California, Berkeley, USA
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=====================================================================
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Subroutine */ int igraphdlarrc_(char *jobt, integer *n, doublereal *vl,
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doublereal *vu, doublereal *d__, doublereal *e, doublereal *pivmin,
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integer *eigcnt, integer *lcnt, integer *rcnt, integer *info)
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{
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/* System generated locals */
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integer i__1;
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doublereal d__1;
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/* Local variables */
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integer i__;
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doublereal sl, su, tmp, tmp2;
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logical matt;
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extern logical igraphlsame_(char *, char *);
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doublereal lpivot, rpivot;
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/* -- LAPACK auxiliary routine (version 3.4.2) --
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-- LAPACK is a software package provided by Univ. of Tennessee, --
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-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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September 2012
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=====================================================================
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Parameter adjustments */
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--e;
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--d__;
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/* Function Body */
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*info = 0;
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*lcnt = 0;
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*rcnt = 0;
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*eigcnt = 0;
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matt = igraphlsame_(jobt, "T");
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if (matt) {
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/* Sturm sequence count on T */
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lpivot = d__[1] - *vl;
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rpivot = d__[1] - *vu;
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if (lpivot <= 0.) {
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++(*lcnt);
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}
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if (rpivot <= 0.) {
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++(*rcnt);
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}
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i__1 = *n - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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/* Computing 2nd power */
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d__1 = e[i__];
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tmp = d__1 * d__1;
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lpivot = d__[i__ + 1] - *vl - tmp / lpivot;
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rpivot = d__[i__ + 1] - *vu - tmp / rpivot;
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if (lpivot <= 0.) {
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++(*lcnt);
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}
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if (rpivot <= 0.) {
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++(*rcnt);
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}
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/* L10: */
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}
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} else {
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/* Sturm sequence count on L D L^T */
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sl = -(*vl);
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su = -(*vu);
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i__1 = *n - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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lpivot = d__[i__] + sl;
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rpivot = d__[i__] + su;
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if (lpivot <= 0.) {
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++(*lcnt);
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}
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if (rpivot <= 0.) {
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++(*rcnt);
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}
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tmp = e[i__] * d__[i__] * e[i__];
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tmp2 = tmp / lpivot;
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if (tmp2 == 0.) {
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sl = tmp - *vl;
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} else {
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sl = sl * tmp2 - *vl;
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}
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tmp2 = tmp / rpivot;
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if (tmp2 == 0.) {
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su = tmp - *vu;
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} else {
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su = su * tmp2 - *vu;
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}
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/* L20: */
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}
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lpivot = d__[*n] + sl;
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rpivot = d__[*n] + su;
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if (lpivot <= 0.) {
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++(*lcnt);
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}
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if (rpivot <= 0.) {
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++(*rcnt);
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}
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}
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*eigcnt = *rcnt - *lcnt;
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return 0;
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/* end of DLARRC */
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} /* igraphdlarrc_ */
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