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template_lapack_larrc.h
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1/* Ergo, version 3.8.2, a program for linear scaling electronic structure
2 * calculations.
3 * Copyright (C) 2023 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
4 * and Anastasia Kruchinina.
5 *
6 * This program is free software: you can redistribute it and/or modify
7 * it under the terms of the GNU General Public License as published by
8 * the Free Software Foundation, either version 3 of the License, or
9 * (at your option) any later version.
10 *
11 * This program is distributed in the hope that it will be useful,
12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 * GNU General Public License for more details.
15 *
16 * You should have received a copy of the GNU General Public License
17 * along with this program. If not, see <http://www.gnu.org/licenses/>.
18 *
19 * Primary academic reference:
20 * Ergo: An open-source program for linear-scaling electronic structure
21 * calculations,
22 * Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
23 * Kruchinina,
24 * SoftwareX 7, 107 (2018),
25 * <http://dx.doi.org/10.1016/j.softx.2018.03.005>
26 *
27 * For further information about Ergo, see <http://www.ergoscf.org>.
28 */
29
30 /* This file belongs to the template_lapack part of the Ergo source
31 * code. The source files in the template_lapack directory are modified
32 * versions of files originally distributed as CLAPACK, see the
33 * Copyright/license notice in the file template_lapack/COPYING.
34 */
35
36
37#ifndef TEMPLATE_LAPACK_LARRC_HEADER
38#define TEMPLATE_LAPACK_LARRC_HEADER
39
40template<class Treal>
41int template_lapack_larrc(const char *jobt, const integer *n, const Treal *vl,
42 const Treal *vu, Treal *d__, Treal *e, Treal *pivmin,
43 integer *eigcnt, integer *lcnt, integer *rcnt, integer *info)
44{
45 /* System generated locals */
46 integer i__1;
47 Treal d__1;
48
49 /* Local variables */
50 integer i__;
51 Treal sl, su, tmp, tmp2;
52 logical matt;
53 Treal lpivot, rpivot;
54
55
56/* -- LAPACK auxiliary routine (version 3.2) -- */
57/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
58/* November 2006 */
59
60/* .. Scalar Arguments .. */
61/* .. */
62/* .. Array Arguments .. */
63/* .. */
64
65/* Purpose */
66/* ======= */
67
68/* Find the number of eigenvalues of the symmetric tridiagonal matrix T */
69/* that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T */
70/* if JOBT = 'L'. */
71
72/* Arguments */
73/* ========= */
74
75/* JOBT (input) CHARACTER*1 */
76/* = 'T': Compute Sturm count for matrix T. */
77/* = 'L': Compute Sturm count for matrix L D L^T. */
78
79/* N (input) INTEGER */
80/* The order of the matrix. N > 0. */
81
82/* VL (input) DOUBLE PRECISION */
83/* VU (input) DOUBLE PRECISION */
84/* The lower and upper bounds for the eigenvalues. */
85
86/* D (input) DOUBLE PRECISION array, dimension (N) */
87/* JOBT = 'T': The N diagonal elements of the tridiagonal matrix T. */
88/* JOBT = 'L': The N diagonal elements of the diagonal matrix D. */
89
90/* E (input) DOUBLE PRECISION array, dimension (N) */
91/* JOBT = 'T': The N-1 offdiagonal elements of the matrix T. */
92/* JOBT = 'L': The N-1 offdiagonal elements of the matrix L. */
93
94/* PIVMIN (input) DOUBLE PRECISION */
95/* The minimum pivot in the Sturm sequence for T. */
96
97/* EIGCNT (output) INTEGER */
98/* The number of eigenvalues of the symmetric tridiagonal matrix T */
99/* that are in the interval (VL,VU] */
100
101/* LCNT (output) INTEGER */
102/* RCNT (output) INTEGER */
103/* The left and right negcounts of the interval. */
104
105/* INFO (output) INTEGER */
106
107/* Further Details */
108/* =============== */
109
110/* Based on contributions by */
111/* Beresford Parlett, University of California, Berkeley, USA */
112/* Jim Demmel, University of California, Berkeley, USA */
113/* Inderjit Dhillon, University of Texas, Austin, USA */
114/* Osni Marques, LBNL/NERSC, USA */
115/* Christof Voemel, University of California, Berkeley, USA */
116
117/* ===================================================================== */
118
119/* .. Parameters .. */
120/* .. */
121/* .. Local Scalars .. */
122/* .. */
123/* .. External Functions .. */
124/* .. */
125/* .. Executable Statements .. */
126
127 /* Parameter adjustments */
128 --e;
129 --d__;
130
131 /* Function Body */
132 *info = 0;
133 *lcnt = 0;
134 *rcnt = 0;
135 *eigcnt = 0;
136 matt = template_blas_lsame(jobt, "T");
137 if (matt) {
138/* Sturm sequence count on T */
139 lpivot = d__[1] - *vl;
140 rpivot = d__[1] - *vu;
141 if (lpivot <= 0.) {
142 ++(*lcnt);
143 }
144 if (rpivot <= 0.) {
145 ++(*rcnt);
146 }
147 i__1 = *n - 1;
148 for (i__ = 1; i__ <= i__1; ++i__) {
149/* Computing 2nd power */
150 d__1 = e[i__];
151 tmp = d__1 * d__1;
152 lpivot = d__[i__ + 1] - *vl - tmp / lpivot;
153 rpivot = d__[i__ + 1] - *vu - tmp / rpivot;
154 if (lpivot <= 0.) {
155 ++(*lcnt);
156 }
157 if (rpivot <= 0.) {
158 ++(*rcnt);
159 }
160/* L10: */
161 }
162 } else {
163/* Sturm sequence count on L D L^T */
164 sl = -(*vl);
165 su = -(*vu);
166 i__1 = *n - 1;
167 for (i__ = 1; i__ <= i__1; ++i__) {
168 lpivot = d__[i__] + sl;
169 rpivot = d__[i__] + su;
170 if (lpivot <= 0.) {
171 ++(*lcnt);
172 }
173 if (rpivot <= 0.) {
174 ++(*rcnt);
175 }
176 tmp = e[i__] * d__[i__] * e[i__];
177
178 tmp2 = tmp / lpivot;
179 if (tmp2 == 0.) {
180 sl = tmp - *vl;
181 } else {
182 sl = sl * tmp2 - *vl;
183 }
184
185 tmp2 = tmp / rpivot;
186 if (tmp2 == 0.) {
187 su = tmp - *vu;
188 } else {
189 su = su * tmp2 - *vu;
190 }
191/* L20: */
192 }
193 lpivot = d__[*n] + sl;
194 rpivot = d__[*n] + su;
195 if (lpivot <= 0.) {
196 ++(*lcnt);
197 }
198 if (rpivot <= 0.) {
199 ++(*rcnt);
200 }
201 }
202 *eigcnt = *rcnt - *lcnt;
203 return 0;
204
205/* end of DLARRC */
206
207} /* dlarrc_ */
208
209#endif
logical template_blas_lsame(const char *ca, const char *cb)
Definition: template_blas_common.cc:46
int integer
Definition: template_blas_common.h:40
bool logical
Definition: template_blas_common.h:41
int template_lapack_larrc(const char *jobt, const integer *n, const Treal *vl, const Treal *vu, Treal *d__, Treal *e, Treal *pivmin, integer *eigcnt, integer *lcnt, integer *rcnt, integer *info)
Definition: template_lapack_larrc.h:41