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
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
|
/* 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_LARFT_HEADER
#define TEMPLATE_LAPACK_LARFT_HEADER
template<class Treal>
int template_lapack_larft(const char *direct, const char *storev, const integer *n, const integer *
k, Treal *v, const integer *ldv, const Treal *tau, Treal *t,
const integer *ldt)
{
/* -- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
DLARFT forms the triangular factor T of a real block reflector H
of order n, which is defined as a product of k elementary reflectors.
If DIRECT = 'F', H = H(1) H(2) . . . H(k) and T is upper triangular;
If DIRECT = 'B', H = H(k) . . . H(2) H(1) and T is lower triangular.
If STOREV = 'C', the vector which defines the elementary reflector
H(i) is stored in the i-th column of the array V, and
H = I - V * T * V'
If STOREV = 'R', the vector which defines the elementary reflector
H(i) is stored in the i-th row of the array V, and
H = I - V' * T * V
Arguments
=========
DIRECT (input) CHARACTER*1
Specifies the order in which the elementary reflectors are
multiplied to form the block reflector:
= 'F': H = H(1) H(2) . . . H(k) (Forward)
= 'B': H = H(k) . . . H(2) H(1) (Backward)
STOREV (input) CHARACTER*1
Specifies how the vectors which define the elementary
reflectors are stored (see also Further Details):
= 'C': columnwise
= 'R': rowwise
N (input) INTEGER
The order of the block reflector H. N >= 0.
K (input) INTEGER
The order of the triangular factor T (= the number of
elementary reflectors). K >= 1.
V (input/output) DOUBLE PRECISION array, dimension
(LDV,K) if STOREV = 'C'
(LDV,N) if STOREV = 'R'
The matrix V. See further details.
LDV (input) INTEGER
The leading dimension of the array V.
If STOREV = 'C', LDV >= max(1,N); if STOREV = 'R', LDV >= K.
TAU (input) DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary
reflector H(i).
T (output) DOUBLE PRECISION array, dimension (LDT,K)
The k by k triangular factor T of the block reflector.
If DIRECT = 'F', T is upper triangular; if DIRECT = 'B', T is
lower triangular. The rest of the array is not used.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= K.
Further Details
===============
The shape of the matrix V and the storage of the vectors which define
the H(i) is best illustrated by the following example with n = 5 and
k = 3. The elements equal to 1 are not stored; the corresponding
array elements are modified but restored on exit. The rest of the
array is not used.
DIRECT = 'F' and STOREV = 'C': DIRECT = 'F' and STOREV = 'R':
V = ( 1 ) V = ( 1 v1 v1 v1 v1 )
( v1 1 ) ( 1 v2 v2 v2 )
( v1 v2 1 ) ( 1 v3 v3 )
( v1 v2 v3 )
( v1 v2 v3 )
DIRECT = 'B' and STOREV = 'C': DIRECT = 'B' and STOREV = 'R':
V = ( v1 v2 v3 ) V = ( v1 v1 1 )
( v1 v2 v3 ) ( v2 v2 v2 1 )
( 1 v2 v3 ) ( v3 v3 v3 v3 1 )
( 1 v3 )
( 1 )
=====================================================================
Quick return if possible
Parameter adjustments */
/* Table of constant values */
integer c__1 = 1;
Treal c_b8 = 0.;
/* System generated locals */
integer t_dim1, t_offset, v_dim1, v_offset, i__1, i__2, i__3;
Treal d__1;
/* Local variables */
integer i__, j;
Treal vii;
#define t_ref(a_1,a_2) t[(a_2)*t_dim1 + a_1]
#define v_ref(a_1,a_2) v[(a_2)*v_dim1 + a_1]
v_dim1 = *ldv;
v_offset = 1 + v_dim1 * 1;
v -= v_offset;
--tau;
t_dim1 = *ldt;
t_offset = 1 + t_dim1 * 1;
t -= t_offset;
/* Function Body */
if (*n == 0) {
return 0;
}
if (template_blas_lsame(direct, "F")) {
i__1 = *k;
for (i__ = 1; i__ <= i__1; ++i__) {
if (tau[i__] == 0.) {
/* H(i) = I */
i__2 = i__;
for (j = 1; j <= i__2; ++j) {
t_ref(j, i__) = 0.;
/* L10: */
}
} else {
/* general case */
vii = v_ref(i__, i__);
v_ref(i__, i__) = 1.;
if (template_blas_lsame(storev, "C")) {
/* T(1:i-1,i) := - tau(i) * V(i:n,1:i-1)' * V(i:n,i) */
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
d__1 = -tau[i__];
template_blas_gemv("Transpose", &i__2, &i__3, &d__1, &v_ref(i__, 1),
ldv, &v_ref(i__, i__), &c__1, &c_b8, &t_ref(1,
i__), &c__1);
} else {
/* T(1:i-1,i) := - tau(i) * V(1:i-1,i:n) * V(i,i:n)' */
i__2 = i__ - 1;
i__3 = *n - i__ + 1;
d__1 = -tau[i__];
template_blas_gemv("No transpose", &i__2, &i__3, &d__1, &v_ref(1, i__)
, ldv, &v_ref(i__, i__), ldv, &c_b8, &t_ref(1,
i__), &c__1);
}
v_ref(i__, i__) = vii;
/* T(1:i-1,i) := T(1:i-1,1:i-1) * T(1:i-1,i) */
i__2 = i__ - 1;
template_blas_trmv("Upper", "No transpose", "Non-unit", &i__2, &t[
t_offset], ldt, &t_ref(1, i__), &c__1);
t_ref(i__, i__) = tau[i__];
}
/* L20: */
}
} else {
for (i__ = *k; i__ >= 1; --i__) {
if (tau[i__] == 0.) {
/* H(i) = I */
i__1 = *k;
for (j = i__; j <= i__1; ++j) {
t_ref(j, i__) = 0.;
/* L30: */
}
} else {
/* general case */
if (i__ < *k) {
if (template_blas_lsame(storev, "C")) {
vii = v_ref(*n - *k + i__, i__);
v_ref(*n - *k + i__, i__) = 1.;
/* T(i+1:k,i) :=
- tau(i) * V(1:n-k+i,i+1:k)' * V(1:n-k+i,i) */
i__1 = *n - *k + i__;
i__2 = *k - i__;
d__1 = -tau[i__];
template_blas_gemv("Transpose", &i__1, &i__2, &d__1, &v_ref(1,
i__ + 1), ldv, &v_ref(1, i__), &c__1, &c_b8, &
t_ref(i__ + 1, i__), &c__1);
v_ref(*n - *k + i__, i__) = vii;
} else {
vii = v_ref(i__, *n - *k + i__);
v_ref(i__, *n - *k + i__) = 1.;
/* T(i+1:k,i) :=
- tau(i) * V(i+1:k,1:n-k+i) * V(i,1:n-k+i)' */
i__1 = *k - i__;
i__2 = *n - *k + i__;
d__1 = -tau[i__];
template_blas_gemv("No transpose", &i__1, &i__2, &d__1, &v_ref(
i__ + 1, 1), ldv, &v_ref(i__, 1), ldv, &c_b8,
&t_ref(i__ + 1, i__), &c__1);
v_ref(i__, *n - *k + i__) = vii;
}
/* T(i+1:k,i) := T(i+1:k,i+1:k) * T(i+1:k,i) */
i__1 = *k - i__;
template_blas_trmv("Lower", "No transpose", "Non-unit", &i__1, &t_ref(
i__ + 1, i__ + 1), ldt, &t_ref(i__ + 1, i__), &
c__1);
}
t_ref(i__, i__) = tau[i__];
}
/* L40: */
}
}
return 0;
/* End of DLARFT */
} /* dlarft_ */
#undef v_ref
#undef t_ref
#endif
|
