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
|
/* 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_ORGTR_HEADER
#define TEMPLATE_LAPACK_ORGTR_HEADER
template<class Treal>
int template_lapack_orgtr(const char *uplo, const integer *n, Treal *a, const integer *
lda, const Treal *tau, Treal *work, const integer *lwork, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
June 30, 1999
Purpose
=======
DORGTR generates a real orthogonal matrix Q which is defined as the
product of n-1 elementary reflectors of order N, as returned by
DSYTRD:
if UPLO = 'U', Q = H(n-1) . . . H(2) H(1),
if UPLO = 'L', Q = H(1) H(2) . . . H(n-1).
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A contains elementary reflectors
from DSYTRD;
= 'L': Lower triangle of A contains elementary reflectors
from DSYTRD.
N (input) INTEGER
The order of the matrix Q. N >= 0.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the vectors which define the elementary reflectors,
as returned by DSYTRD.
On exit, the N-by-N orthogonal matrix Q.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
TAU (input) DOUBLE PRECISION array, dimension (N-1)
TAU(i) must contain the scalar factor of the elementary
reflector H(i), as returned by DSYTRD.
WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,N-1).
For optimum performance LWORK >= (N-1)*NB, where NB is
the optimal blocksize.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input arguments
Parameter adjustments */
/* Table of constant values */
integer c__1 = 1;
integer c_n1 = -1;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
/* Local variables */
integer i__, j;
integer iinfo;
logical upper;
integer nb;
integer lwkopt;
logical lquery;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--tau;
--work;
/* Initialization added by Elias to get rid of compiler warnings. */
lwkopt = 0;
/* Function Body */
*info = 0;
lquery = *lwork == -1;
upper = template_blas_lsame(uplo, "U");
if (! upper && ! template_blas_lsame(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < maxMACRO(1,*n)) {
*info = -4;
} else /* if(complicated condition) */ {
/* Computing MAX */
i__1 = 1, i__2 = *n - 1;
if (*lwork < maxMACRO(i__1,i__2) && ! lquery) {
*info = -7;
}
}
if (*info == 0) {
if (upper) {
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
nb = template_lapack_ilaenv(&c__1, "DORGQL", " ", &i__1, &i__2, &i__3, &c_n1, (
ftnlen)6, (ftnlen)1);
} else {
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
nb = template_lapack_ilaenv(&c__1, "DORGQR", " ", &i__1, &i__2, &i__3, &c_n1, (
ftnlen)6, (ftnlen)1);
}
/* Computing MAX */
i__1 = 1, i__2 = *n - 1;
lwkopt = maxMACRO(i__1,i__2) * nb;
work[1] = (Treal) lwkopt;
}
if (*info != 0) {
i__1 = -(*info);
template_blas_erbla("ORGTR ", &i__1);
return 0;
} else if (lquery) {
return 0;
}
/* Quick return if possible */
if (*n == 0) {
work[1] = 1.;
return 0;
}
if (upper) {
/* Q was determined by a call to DSYTRD with UPLO = 'U'
Shift the vectors which define the elementary reflectors one
column to the left, and set the last row and column of Q to
those of the unit matrix */
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
a_ref(i__, j) = a_ref(i__, j + 1);
/* L10: */
}
a_ref(*n, j) = 0.;
/* L20: */
}
i__1 = *n - 1;
for (i__ = 1; i__ <= i__1; ++i__) {
a_ref(i__, *n) = 0.;
/* L30: */
}
a_ref(*n, *n) = 1.;
/* Generate Q(1:n-1,1:n-1) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
template_lapack_orgql(&i__1, &i__2, &i__3, &a[a_offset], lda, &tau[1], &work[1],
lwork, &iinfo);
} else {
/* Q was determined by a call to DSYTRD with UPLO = 'L'.
Shift the vectors which define the elementary reflectors one
column to the right, and set the first row and column of Q to
those of the unit matrix */
for (j = *n; j >= 2; --j) {
a_ref(1, j) = 0.;
i__1 = *n;
for (i__ = j + 1; i__ <= i__1; ++i__) {
a_ref(i__, j) = a_ref(i__, j - 1);
/* L40: */
}
/* L50: */
}
a_ref(1, 1) = 1.;
i__1 = *n;
for (i__ = 2; i__ <= i__1; ++i__) {
a_ref(i__, 1) = 0.;
/* L60: */
}
if (*n > 1) {
/* Generate Q(2:n,2:n) */
i__1 = *n - 1;
i__2 = *n - 1;
i__3 = *n - 1;
template_lapack_orgqr(
&i__1,
&i__2,
&i__3,
&a_ref(2, 2),
lda,
&tau[1],
&work[1],
lwork,
&iinfo
);
}
}
work[1] = (Treal) lwkopt;
return 0;
/* End of DORGTR */
} /* dorgtr_ */
#undef a_ref
#endif
|
