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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_LANEG_HEADER
#define TEMPLATE_LAPACK_LANEG_HEADER
#include "template_lapack_isnan.h"
template<class Treal>
int template_lapack_laneg(integer *n, Treal *d__, Treal *lld, Treal *
sigma, Treal *pivmin, integer *r__)
{
/* System generated locals */
integer ret_val, i__1, i__2, i__3, i__4;
/* Local variables */
integer j;
Treal p, t;
integer bj;
Treal tmp;
integer neg1, neg2;
Treal bsav, gamma, dplus;
integer negcnt;
logical sawnan;
Treal dminus;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLANEG computes the Sturm count, the number of negative pivots */
/* encountered while factoring tridiagonal T - sigma I = L D L^T. */
/* This implementation works directly on the factors without forming */
/* the tridiagonal matrix T. The Sturm count is also the number of */
/* eigenvalues of T less than sigma. */
/* This routine is called from DLARRB. */
/* The current routine does not use the PIVMIN parameter but rather */
/* requires IEEE-754 propagation of Infinities and NaNs. This */
/* routine also has no input range restrictions but does require */
/* default exception handling such that x/0 produces Inf when x is */
/* non-zero, and Inf/Inf produces NaN. For more information, see: */
/* Marques, Riedy, and Voemel, "Benefits of IEEE-754 Features in */
/* Modern Symmetric Tridiagonal Eigensolvers," SIAM Journal on */
/* Scientific Computing, v28, n5, 2006. DOI 10.1137/050641624 */
/* (Tech report version in LAWN 172 with the same title.) */
/* Arguments */
/* ========= */
/* N (input) INTEGER */
/* The order of the matrix. */
/* D (input) DOUBLE PRECISION array, dimension (N) */
/* The N diagonal elements of the diagonal matrix D. */
/* LLD (input) DOUBLE PRECISION array, dimension (N-1) */
/* The (N-1) elements L(i)*L(i)*D(i). */
/* SIGMA (input) DOUBLE PRECISION */
/* Shift amount in T - sigma I = L D L^T. */
/* PIVMIN (input) DOUBLE PRECISION */
/* The minimum pivot in the Sturm sequence. May be used */
/* when zero pivots are encountered on non-IEEE-754 */
/* architectures. */
/* R (input) INTEGER */
/* The twist index for the twisted factorization that is used */
/* for the negcount. */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Osni Marques, LBNL/NERSC, USA */
/* Christof Voemel, University of California, Berkeley, USA */
/* Jason Riedy, University of California, Berkeley, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* Some architectures propagate Infinities and NaNs very slowly, so */
/* the code computes counts in BLKLEN chunks. Then a NaN can */
/* propagate at most BLKLEN columns before being detected. This is */
/* not a general tuning parameter; it needs only to be just large */
/* enough that the overhead is tiny in common cases. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--lld;
--d__;
/* Function Body */
negcnt = 0;
/* I) upper part: L D L^T - SIGMA I = L+ D+ L+^T */
t = -(*sigma);
i__1 = *r__ - 1;
for (bj = 1; bj <= i__1; bj += 128) {
neg1 = 0;
bsav = t;
/* Computing MIN */
i__3 = bj + 127, i__4 = *r__ - 1;
i__2 = minMACRO(i__3,i__4);
for (j = bj; j <= i__2; ++j) {
dplus = d__[j] + t;
if (dplus < 0.) {
++neg1;
}
tmp = t / dplus;
t = tmp * lld[j] - *sigma;
/* L21: */
}
sawnan = template_lapack_isnan(&t);
/* Run a slower version of the above loop if a NaN is detected. */
/* A NaN should occur only with a zero pivot after an infinite */
/* pivot. In that case, substituting 1 for T/DPLUS is the */
/* correct limit. */
if (sawnan) {
neg1 = 0;
t = bsav;
/* Computing MIN */
i__3 = bj + 127, i__4 = *r__ - 1;
i__2 = minMACRO(i__3,i__4);
for (j = bj; j <= i__2; ++j) {
dplus = d__[j] + t;
if (dplus < 0.) {
++neg1;
}
tmp = t / dplus;
if (template_lapack_isnan(&tmp)) {
tmp = 1.;
}
t = tmp * lld[j] - *sigma;
/* L22: */
}
}
negcnt += neg1;
/* L210: */
}
/* II) lower part: L D L^T - SIGMA I = U- D- U-^T */
p = d__[*n] - *sigma;
i__1 = *r__;
for (bj = *n - 1; bj >= i__1; bj += -128) {
neg2 = 0;
bsav = p;
/* Computing MAX */
i__3 = bj - 127;
i__2 = maxMACRO(i__3,*r__);
for (j = bj; j >= i__2; --j) {
dminus = lld[j] + p;
if (dminus < 0.) {
++neg2;
}
tmp = p / dminus;
p = tmp * d__[j] - *sigma;
/* L23: */
}
sawnan = template_lapack_isnan(&p);
/* As above, run a slower version that substitutes 1 for Inf/Inf. */
if (sawnan) {
neg2 = 0;
p = bsav;
/* Computing MAX */
i__3 = bj - 127;
i__2 = maxMACRO(i__3,*r__);
for (j = bj; j >= i__2; --j) {
dminus = lld[j] + p;
if (dminus < 0.) {
++neg2;
}
tmp = p / dminus;
if (template_lapack_isnan(&tmp)) {
tmp = 1.;
}
p = tmp * d__[j] - *sigma;
/* L24: */
}
}
negcnt += neg2;
/* L230: */
}
/* III) Twist index */
/* T was shifted by SIGMA initially. */
gamma = t + *sigma + p;
if (gamma < 0.) {
++negcnt;
}
ret_val = negcnt;
return ret_val;
} /* dlaneg_ */
#endif
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