Add graph references
This commit is contained in:
Abdelrahman Said
+222
@@ -0,0 +1,222 @@
|
||||
/* -- 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 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_ */
|
||||
|
||||
Reference in New Issue
Block a user