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/* dlarrk.f -- translated by f2c (version 20061008).
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"
#include "blaswrap.h"
/* Subroutine */ int dlarrk_(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 dlamch_(char *);
integer negcnt;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* 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. */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the tridiagonal matrix T. N >= 0. */
/* IW (input) INTEGER */
/* The index of the eigenvalues to be returned. */
/* GL (input) DOUBLE PRECISION */
/* GU (input) DOUBLE PRECISION */
/* An upper and a lower bound on the eigenvalue. */
/* D (input) DOUBLE PRECISION array, dimension (N) */
/* The n diagonal elements of the tridiagonal matrix T. */
/* E2 (input) DOUBLE PRECISION array, dimension (N-1) */
/* The (n-1) squared off-diagonal elements of the tridiagonal matrix T. */
/* PIVMIN (input) DOUBLE PRECISION */
/* The minimum pivot allowed in the Sturm sequence for T. */
/* RELTOL (input) 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. */
/* W (output) DOUBLE PRECISION */
/* WERR (output) DOUBLE PRECISION */
/* The error bound on the corresponding eigenvalue approximation */
/* in W. */
/* INFO (output) INTEGER */
/* = 0: Eigenvalue converged */
/* = -1: Eigenvalue did NOT converge */
/* Internal Parameters */
/* =================== */
/* FUDGE DOUBLE PRECISION, default = 2 */
/* A "fudge factor" to widen the Gershgorin intervals. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Get machine constants */
/* Parameter adjustments */
--e2;
--d__;
/* Function Body */
eps = dlamch_("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 */
} /* dlarrk_ */
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