1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
|
/* Ergo, version 3.8.2, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2023 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_LARRC_HEADER
#define TEMPLATE_LAPACK_LARRC_HEADER
template<class Treal>
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)
{
/* System generated locals */
integer i__1;
Treal d__1;
/* Local variables */
integer i__;
Treal sl, su, tmp, tmp2;
logical matt;
Treal lpivot, rpivot;
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* Find the number of eigenvalues of the symmetric tridiagonal matrix T */
/* that are in the interval (VL,VU] if JOBT = 'T', and of L D L^T */
/* if JOBT = 'L'. */
/* Arguments */
/* ========= */
/* JOBT (input) CHARACTER*1 */
/* = 'T': Compute Sturm count for matrix T. */
/* = 'L': Compute Sturm count for matrix L D L^T. */
/* N (input) INTEGER */
/* The order of the matrix. N > 0. */
/* VL (input) DOUBLE PRECISION */
/* VU (input) DOUBLE PRECISION */
/* The lower and upper bounds for the eigenvalues. */
/* D (input) DOUBLE PRECISION array, dimension (N) */
/* JOBT = 'T': The N diagonal elements of the tridiagonal matrix T. */
/* JOBT = 'L': The N diagonal elements of the diagonal matrix D. */
/* E (input) DOUBLE PRECISION array, dimension (N) */
/* JOBT = 'T': The N-1 offdiagonal elements of the matrix T. */
/* JOBT = 'L': The N-1 offdiagonal elements of the matrix L. */
/* PIVMIN (input) DOUBLE PRECISION */
/* The minimum pivot in the Sturm sequence for T. */
/* EIGCNT (output) INTEGER */
/* The number of eigenvalues of the symmetric tridiagonal matrix T */
/* that are in the interval (VL,VU] */
/* LCNT (output) INTEGER */
/* RCNT (output) INTEGER */
/* The left and right negcounts of the interval. */
/* INFO (output) INTEGER */
/* Further Details */
/* =============== */
/* Based on contributions by */
/* Beresford Parlett, University of California, Berkeley, USA */
/* Jim Demmel, University of California, Berkeley, USA */
/* Inderjit Dhillon, University of Texas, Austin, USA */
/* Osni Marques, LBNL/NERSC, USA */
/* Christof Voemel, University of California, Berkeley, USA */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
--e;
--d__;
/* Function Body */
*info = 0;
*lcnt = 0;
*rcnt = 0;
*eigcnt = 0;
matt = template_blas_lsame(jobt, "T");
if (matt) {
/* Sturm sequence count on T */
lpivot = d__[1] - *vl;
rpivot = d__[1] - *vu;
if (lpivot <= 0.) {
++(*lcnt);
}
if (rpivot <= 0.) {
++(*rcnt);
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing 2nd power */
d__1 = e[i__];
tmp = d__1 * d__1;
lpivot = d__[i__ + 1] - *vl - tmp / lpivot;
rpivot = d__[i__ + 1] - *vu - tmp / rpivot;
if (lpivot <= 0.) {
++(*lcnt);
}
if (rpivot <= 0.) {
++(*rcnt);
}
/* L10: */
}
} else {
/* Sturm sequence count on L D L^T */
sl = -(*vl);
su = -(*vu);
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
lpivot = d__[i__] + sl;
rpivot = d__[i__] + su;
if (lpivot <= 0.) {
++(*lcnt);
}
if (rpivot <= 0.) {
++(*rcnt);
}
tmp = e[i__] * d__[i__] * e[i__];
tmp2 = tmp / lpivot;
if (tmp2 == 0.) {
sl = tmp - *vl;
} else {
sl = sl * tmp2 - *vl;
}
tmp2 = tmp / rpivot;
if (tmp2 == 0.) {
su = tmp - *vu;
} else {
su = su * tmp2 - *vu;
}
/* L20: */
}
lpivot = d__[*n] + sl;
rpivot = d__[*n] + su;
if (lpivot <= 0.) {
++(*lcnt);
}
if (rpivot <= 0.) {
++(*rcnt);
}
}
*eigcnt = *rcnt - *lcnt;
return 0;
/* end of DLARRC */
} /* dlarrc_ */
#endif
|
