Add graph references
This commit is contained in:
Abdelrahman Said
+264
@@ -0,0 +1,264 @@
|
||||
/* -- 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 DLARRK computes one eigenvalue of a symmetric tridiagonal matrix T to suitable accuracy.
|
||||
|
||||
=========== DOCUMENTATION ===========
|
||||
|
||||
Online html documentation available at
|
||||
http://www.netlib.org/lapack/explore-html/
|
||||
|
||||
> \htmlonly
|
||||
> Download DLARRK + dependencies
|
||||
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarrk.
|
||||
f">
|
||||
> [TGZ]</a>
|
||||
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarrk.
|
||||
f">
|
||||
> [ZIP]</a>
|
||||
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarrk.
|
||||
f">
|
||||
> [TXT]</a>
|
||||
> \endhtmlonly
|
||||
|
||||
Definition:
|
||||
===========
|
||||
|
||||
SUBROUTINE DLARRK( N, IW, GL, GU,
|
||||
D, E2, PIVMIN, RELTOL, W, WERR, INFO)
|
||||
|
||||
INTEGER INFO, IW, N
|
||||
DOUBLE PRECISION PIVMIN, RELTOL, GL, GU, W, WERR
|
||||
DOUBLE PRECISION D( * ), E2( * )
|
||||
|
||||
|
||||
> \par Purpose:
|
||||
=============
|
||||
>
|
||||
> \verbatim
|
||||
>
|
||||
> DLARRK computes one eigenvalue of a symmetric tridiagonal
|
||||
> matrix T to suitable accuracy. This is an auxiliary code to be
|
||||
> called from DSTEMR.
|
||||
>
|
||||
> To avoid overflow, the matrix must be scaled so that its
|
||||
> largest element is no greater than overflow**(1/2) * underflow**(1/4) in absolute value, and for greatest
|
||||
|
||||
> accuracy, it should not be much smaller than that.
|
||||
>
|
||||
> See W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal
|
||||
> Matrix", Report CS41, Computer Science Dept., Stanford
|
||||
> University, July 21, 1966.
|
||||
> \endverbatim
|
||||
|
||||
Arguments:
|
||||
==========
|
||||
|
||||
> \param[in] N
|
||||
> \verbatim
|
||||
> N is INTEGER
|
||||
> The order of the tridiagonal matrix T. N >= 0.
|
||||
> \endverbatim
|
||||
>
|
||||
> \param[in] IW
|
||||
> \verbatim
|
||||
> IW is INTEGER
|
||||
> The index of the eigenvalues to be returned.
|
||||
> \endverbatim
|
||||
>
|
||||
> \param[in] GL
|
||||
> \verbatim
|
||||
> GL is DOUBLE PRECISION
|
||||
> \endverbatim
|
||||
>
|
||||
> \param[in] GU
|
||||
> \verbatim
|
||||
> GU is DOUBLE PRECISION
|
||||
> An upper and a lower bound on the eigenvalue.
|
||||
> \endverbatim
|
||||
>
|
||||
> \param[in] D
|
||||
> \verbatim
|
||||
> D is DOUBLE PRECISION array, dimension (N)
|
||||
> The n diagonal elements of the tridiagonal matrix T.
|
||||
> \endverbatim
|
||||
>
|
||||
> \param[in] E2
|
||||
> \verbatim
|
||||
> E2 is DOUBLE PRECISION array, dimension (N-1)
|
||||
> The (n-1) squared off-diagonal elements of the tridiagonal matrix T.
|
||||
> \endverbatim
|
||||
>
|
||||
> \param[in] PIVMIN
|
||||
> \verbatim
|
||||
> PIVMIN is DOUBLE PRECISION
|
||||
> The minimum pivot allowed in the Sturm sequence for T.
|
||||
> \endverbatim
|
||||
>
|
||||
> \param[in] RELTOL
|
||||
> \verbatim
|
||||
> RELTOL is DOUBLE PRECISION
|
||||
> The minimum relative width of an interval. When an interval
|
||||
> is narrower than RELTOL times the larger (in
|
||||
> magnitude) endpoint, then it is considered to be
|
||||
> sufficiently small, i.e., converged. Note: this should
|
||||
> always be at least radix*machine epsilon.
|
||||
> \endverbatim
|
||||
>
|
||||
> \param[out] W
|
||||
> \verbatim
|
||||
> W is DOUBLE PRECISION
|
||||
> \endverbatim
|
||||
>
|
||||
> \param[out] WERR
|
||||
> \verbatim
|
||||
> WERR is DOUBLE PRECISION
|
||||
> The error bound on the corresponding eigenvalue approximation
|
||||
> in W.
|
||||
> \endverbatim
|
||||
>
|
||||
> \param[out] INFO
|
||||
> \verbatim
|
||||
> INFO is INTEGER
|
||||
> = 0: Eigenvalue converged
|
||||
> = -1: Eigenvalue did NOT converge
|
||||
> \endverbatim
|
||||
|
||||
> \par Internal Parameters:
|
||||
=========================
|
||||
>
|
||||
> \verbatim
|
||||
> FUDGE DOUBLE PRECISION, default = 2
|
||||
> A "fudge factor" to widen the Gershgorin intervals.
|
||||
> \endverbatim
|
||||
|
||||
Authors:
|
||||
========
|
||||
|
||||
> \author Univ. of Tennessee
|
||||
> \author Univ. of California Berkeley
|
||||
> \author Univ. of Colorado Denver
|
||||
> \author NAG Ltd.
|
||||
|
||||
> \date September 2012
|
||||
|
||||
> \ingroup auxOTHERauxiliary
|
||||
|
||||
=====================================================================
|
||||
Subroutine */ int igraphdlarrk_(integer *n, integer *iw, doublereal *gl,
|
||||
doublereal *gu, doublereal *d__, doublereal *e2, doublereal *pivmin,
|
||||
doublereal *reltol, doublereal *w, doublereal *werr, integer *info)
|
||||
{
|
||||
/* System generated locals */
|
||||
integer i__1;
|
||||
doublereal d__1, d__2;
|
||||
|
||||
/* Builtin functions */
|
||||
double log(doublereal);
|
||||
|
||||
/* Local variables */
|
||||
integer i__, it;
|
||||
doublereal mid, eps, tmp1, tmp2, left, atoli, right;
|
||||
integer itmax;
|
||||
doublereal rtoli, tnorm;
|
||||
extern doublereal igraphdlamch_(char *);
|
||||
integer negcnt;
|
||||
|
||||
|
||||
/* -- 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
|
||||
|
||||
|
||||
=====================================================================
|
||||
|
||||
|
||||
Get machine constants
|
||||
Parameter adjustments */
|
||||
--e2;
|
||||
--d__;
|
||||
|
||||
/* Function Body */
|
||||
eps = igraphdlamch_("P");
|
||||
/* Computing MAX */
|
||||
d__1 = abs(*gl), d__2 = abs(*gu);
|
||||
tnorm = max(d__1,d__2);
|
||||
rtoli = *reltol;
|
||||
atoli = *pivmin * 4.;
|
||||
itmax = (integer) ((log(tnorm + *pivmin) - log(*pivmin)) / log(2.)) + 2;
|
||||
*info = -1;
|
||||
left = *gl - tnorm * 2. * eps * *n - *pivmin * 4.;
|
||||
right = *gu + tnorm * 2. * eps * *n + *pivmin * 4.;
|
||||
it = 0;
|
||||
L10:
|
||||
|
||||
/* Check if interval converged or maximum number of iterations reached */
|
||||
|
||||
tmp1 = (d__1 = right - left, abs(d__1));
|
||||
/* Computing MAX */
|
||||
d__1 = abs(right), d__2 = abs(left);
|
||||
tmp2 = max(d__1,d__2);
|
||||
/* Computing MAX */
|
||||
d__1 = max(atoli,*pivmin), d__2 = rtoli * tmp2;
|
||||
if (tmp1 < max(d__1,d__2)) {
|
||||
*info = 0;
|
||||
goto L30;
|
||||
}
|
||||
if (it > itmax) {
|
||||
goto L30;
|
||||
}
|
||||
|
||||
/* Count number of negative pivots for mid-point */
|
||||
|
||||
++it;
|
||||
mid = (left + right) * .5;
|
||||
negcnt = 0;
|
||||
tmp1 = d__[1] - mid;
|
||||
if (abs(tmp1) < *pivmin) {
|
||||
tmp1 = -(*pivmin);
|
||||
}
|
||||
if (tmp1 <= 0.) {
|
||||
++negcnt;
|
||||
}
|
||||
|
||||
i__1 = *n;
|
||||
for (i__ = 2; i__ <= i__1; ++i__) {
|
||||
tmp1 = d__[i__] - e2[i__ - 1] / tmp1 - mid;
|
||||
if (abs(tmp1) < *pivmin) {
|
||||
tmp1 = -(*pivmin);
|
||||
}
|
||||
if (tmp1 <= 0.) {
|
||||
++negcnt;
|
||||
}
|
||||
/* L20: */
|
||||
}
|
||||
if (negcnt >= *iw) {
|
||||
right = mid;
|
||||
} else {
|
||||
left = mid;
|
||||
}
|
||||
goto L10;
|
||||
L30:
|
||||
|
||||
/* Converged or maximum number of iterations reached */
|
||||
|
||||
*w = (left + right) * .5;
|
||||
*werr = (d__1 = right - left, abs(d__1)) * .5;
|
||||
return 0;
|
||||
|
||||
/* End of DLARRK */
|
||||
|
||||
} /* igraphdlarrk_ */
|
||||
|
||||
Reference in New Issue
Block a user