Abdelrahman Said
223 lines
6.5 KiB
C
223 lines
6.5 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 DLARRR performs tests to decide whether the symmetric tridiagonal matrix T warrants expensive c
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omputations which guarantee high relative accuracy in the eigenvalues.
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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 DLARRR + dependencies
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> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrr.
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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/dlarrr.
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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/dlarrr.
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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 DLARRR( N, D, E, INFO )
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INTEGER N, INFO
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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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> Perform tests to decide whether the symmetric tridiagonal matrix T
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> warrants expensive computations which guarantee high relative accuracy
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> in the eigenvalues.
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> \endverbatim
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Arguments:
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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] D
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> \verbatim
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> D is DOUBLE PRECISION array, dimension (N)
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> The N diagonal elements of the tridiagonal matrix T.
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> \endverbatim
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>
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> \param[in,out] E
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> \verbatim
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> E is DOUBLE PRECISION array, dimension (N)
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> On entry, the first (N-1) entries contain the subdiagonal
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> elements of the tridiagonal matrix T; E(N) is set to ZERO.
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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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> INFO = 0(default) : the matrix warrants computations preserving
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> relative accuracy.
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> INFO = 1 : the matrix warrants computations guaranteeing
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> only absolute accuracy.
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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 igraphdlarrr_(integer *n, doublereal *d__, doublereal *e,
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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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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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integer i__;
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doublereal eps, tmp, tmp2, rmin;
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extern doublereal igraphdlamch_(char *);
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doublereal offdig, safmin;
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logical yesrel;
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doublereal smlnum, offdig2;
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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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As a default, do NOT go for relative-accuracy preserving computations.
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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 = 1;
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safmin = igraphdlamch_("Safe minimum");
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eps = igraphdlamch_("Precision");
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smlnum = safmin / eps;
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rmin = sqrt(smlnum);
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/* Tests for relative accuracy
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Test for scaled diagonal dominance
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Scale the diagonal entries to one and check whether the sum of the
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off-diagonals is less than one
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The sdd relative error bounds have a 1/(1- 2*x) factor in them,
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x = max(OFFDIG + OFFDIG2), so when x is close to 1/2, no relative
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accuracy is promised. In the notation of the code fragment below,
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1/(1 - (OFFDIG + OFFDIG2)) is the condition number.
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We don't think it is worth going into "sdd mode" unless the relative
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condition number is reasonable, not 1/macheps.
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The threshold should be compatible with other thresholds used in the
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code. We set OFFDIG + OFFDIG2 <= .999 =: RELCOND, it corresponds
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to losing at most 3 decimal digits: 1 / (1 - (OFFDIG + OFFDIG2)) <= 1000
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instead of the current OFFDIG + OFFDIG2 < 1 */
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yesrel = TRUE_;
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offdig = 0.;
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tmp = sqrt((abs(d__[1])));
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if (tmp < rmin) {
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yesrel = FALSE_;
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}
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if (! yesrel) {
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goto L11;
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}
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i__1 = *n;
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for (i__ = 2; i__ <= i__1; ++i__) {
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tmp2 = sqrt((d__1 = d__[i__], abs(d__1)));
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if (tmp2 < rmin) {
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yesrel = FALSE_;
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}
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if (! yesrel) {
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goto L11;
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}
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offdig2 = (d__1 = e[i__ - 1], abs(d__1)) / (tmp * tmp2);
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if (offdig + offdig2 >= .999) {
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yesrel = FALSE_;
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}
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if (! yesrel) {
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goto L11;
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}
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tmp = tmp2;
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offdig = offdig2;
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/* L10: */
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}
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L11:
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if (yesrel) {
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*info = 0;
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return 0;
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} else {
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}
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/* *** MORE TO BE IMPLEMENTED ***
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Test if the lower bidiagonal matrix L from T = L D L^T
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(zero shift facto) is well conditioned
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Test if the upper bidiagonal matrix U from T = U D U^T
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(zero shift facto) is well conditioned.
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In this case, the matrix needs to be flipped and, at the end
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of the eigenvector computation, the flip needs to be applied
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to the computed eigenvectors (and the support) */
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return 0;
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/* END OF DLARRR */
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} /* igraphdlarrr_ */
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