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/* Ergo, version 3.8, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2019 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
* and Anastasia Kruchinina.
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* Primary academic reference:
* Ergo: An open-source program for linear-scaling electronic structure
* calculations,
* Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
* Kruchinina,
* SoftwareX 7, 107 (2018),
* <http://dx.doi.org/10.1016/j.softx.2018.03.005>
*
* For further information about Ergo, see <http://www.ergoscf.org>.
*/
/* This file belongs to the template_lapack part of the Ergo source
* code. The source files in the template_lapack directory are modified
* versions of files originally distributed as CLAPACK, see the
* Copyright/license notice in the file template_lapack/COPYING.
*/
#ifndef TEMPLATE_LAPACK_LARRK_HEADER
#define TEMPLATE_LAPACK_LARRK_HEADER
template<class Treal>
int template_lapack_larrk(integer *n, integer *iw, Treal *gl,
Treal *gu, Treal *d__, Treal *e2, Treal *pivmin,
Treal *reltol, Treal *w, Treal *werr, integer *info)
{
/* System generated locals */
integer i__1;
Treal d__1, d__2;
/* Local variables */
integer i__, it;
Treal mid, eps, tmp1, tmp2, left, atoli, right;
integer itmax;
Treal rtoli, tnorm;
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 = template_lapack_lamch("P", (Treal)0);
/* Computing MAX */
d__1 = absMACRO(*gl), d__2 = absMACRO(*gu);
tnorm = maxMACRO(d__1,d__2);
rtoli = *reltol;
atoli = *pivmin * 4.;
itmax = (integer) ((template_blas_log(tnorm + *pivmin) - template_blas_log(*pivmin)) / template_blas_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, absMACRO(d__1));
/* Computing MAX */
d__1 = absMACRO(right), d__2 = absMACRO(left);
tmp2 = maxMACRO(d__1,d__2);
/* Computing MAX */
d__1 = maxMACRO(atoli,*pivmin), d__2 = rtoli * tmp2;
if (tmp1 < maxMACRO(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 (absMACRO(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 (absMACRO(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, absMACRO(d__1)) * .5;
return 0;
/* End of DLARRK */
} /* dlarrk_ */
#endif
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