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
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
|
/* 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_BLAS_TRSM_HEADER
#define TEMPLATE_BLAS_TRSM_HEADER
#include "template_blas_common.h"
template<class Treal>
int template_blas_trsm(const char *side, const char *uplo, const char *transa, const char *diag,
const integer *m, const integer *n, const Treal *alpha, const Treal *a, const integer *
lda, Treal *b, const integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
integer info;
Treal temp;
integer i__, j, k;
logical lside;
integer nrowa;
logical upper;
logical nounit;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
/* Purpose
=======
DTRSM solves one of the matrix equations
op( A )*X = alpha*B, or X*op( A ) = alpha*B,
where alpha is a scalar, X and B are m by n matrices, A is a unit, or
non-unit, upper or lower triangular matrix and op( A ) is one of
op( A ) = A or op( A ) = A'.
The matrix X is overwritten on B.
Parameters
==========
SIDE - CHARACTER*1.
On entry, SIDE specifies whether op( A ) appears on the left
or right of X as follows:
SIDE = 'L' or 'l' op( A )*X = alpha*B.
SIDE = 'R' or 'r' X*op( A ) = alpha*B.
Unchanged on exit.
UPLO - CHARACTER*1.
On entry, UPLO specifies whether the matrix A is an upper or
lower triangular matrix as follows:
UPLO = 'U' or 'u' A is an upper triangular matrix.
UPLO = 'L' or 'l' A is a lower triangular matrix.
Unchanged on exit.
TRANSA - CHARACTER*1.
On entry, TRANSA specifies the form of op( A ) to be used in
the matrix multiplication as follows:
TRANSA = 'N' or 'n' op( A ) = A.
TRANSA = 'T' or 't' op( A ) = A'.
TRANSA = 'C' or 'c' op( A ) = A'.
Unchanged on exit.
DIAG - CHARACTER*1.
On entry, DIAG specifies whether or not A is unit triangular
as follows:
DIAG = 'U' or 'u' A is assumed to be unit triangular.
DIAG = 'N' or 'n' A is not assumed to be unit
triangular.
Unchanged on exit.
M - INTEGER.
On entry, M specifies the number of rows of B. M must be at
least zero.
Unchanged on exit.
N - INTEGER.
On entry, N specifies the number of columns of B. N must be
at least zero.
Unchanged on exit.
ALPHA - DOUBLE PRECISION.
On entry, ALPHA specifies the scalar alpha. When alpha is
zero then A is not referenced and B need not be set before
entry.
Unchanged on exit.
A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m
when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'.
Before entry with UPLO = 'U' or 'u', the leading k by k
upper triangular part of the array A must contain the upper
triangular matrix and the strictly lower triangular part of
A is not referenced.
Before entry with UPLO = 'L' or 'l', the leading k by k
lower triangular part of the array A must contain the lower
triangular matrix and the strictly upper triangular part of
A is not referenced.
Note that when DIAG = 'U' or 'u', the diagonal elements of
A are not referenced either, but are assumed to be unity.
Unchanged on exit.
LDA - INTEGER.
On entry, LDA specifies the first dimension of A as declared
in the calling (sub) program. When SIDE = 'L' or 'l' then
LDA must be at least max( 1, m ), when SIDE = 'R' or 'r'
then LDA must be at least max( 1, n ).
Unchanged on exit.
B - DOUBLE PRECISION array of DIMENSION ( LDB, n ).
Before entry, the leading m by n part of the array B must
contain the right-hand side matrix B, and on exit is
overwritten by the solution matrix X.
LDB - INTEGER.
On entry, LDB specifies the first dimension of B as declared
in the calling (sub) program. LDB must be at least
max( 1, m ).
Unchanged on exit.
Level 3 Blas routine.
-- Written on 8-February-1989.
Jack Dongarra, Argonne National Laboratory.
Iain Duff, AERE Harwell.
Jeremy Du Croz, Numerical Algorithms Group Ltd.
Sven Hammarling, Numerical Algorithms Group Ltd.
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* Function Body */
lside = template_blas_lsame(side, "L");
if (lside) {
nrowa = *m;
} else {
nrowa = *n;
}
nounit = template_blas_lsame(diag, "N");
upper = template_blas_lsame(uplo, "U");
info = 0;
if (! lside && ! template_blas_lsame(side, "R")) {
info = 1;
} else if (! upper && ! template_blas_lsame(uplo, "L")) {
info = 2;
} else if (! template_blas_lsame(transa, "N") && ! template_blas_lsame(transa,
"T") && ! template_blas_lsame(transa, "C")) {
info = 3;
} else if (! template_blas_lsame(diag, "U") && ! template_blas_lsame(diag,
"N")) {
info = 4;
} else if (*m < 0) {
info = 5;
} else if (*n < 0) {
info = 6;
} else if (*lda < maxMACRO(1,nrowa)) {
info = 9;
} else if (*ldb < maxMACRO(1,*m)) {
info = 11;
}
if (info != 0) {
template_blas_erbla("TRSM ", &info);
return 0;
}
/* Quick return if possible. */
if (*n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = 0.;
/* L10: */
}
/* L20: */
}
return 0;
}
/* Start the operations. */
if (lside) {
if (template_blas_lsame(transa, "N")) {
/* Form B := alpha*inv( A )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = *alpha * b_ref(i__, j);
/* L30: */
}
}
for (k = *m; k >= 1; --k) {
if (b_ref(k, j) != 0.) {
if (nounit) {
b_ref(k, j) = b_ref(k, j) / a_ref(k, k);
}
i__2 = k - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = b_ref(i__, j) - b_ref(k, j) *
a_ref(i__, k);
/* L40: */
}
}
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = *alpha * b_ref(i__, j);
/* L70: */
}
}
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
if (b_ref(k, j) != 0.) {
if (nounit) {
b_ref(k, j) = b_ref(k, j) / a_ref(k, k);
}
i__3 = *m;
for (i__ = k + 1; i__ <= i__3; ++i__) {
b_ref(i__, j) = b_ref(i__, j) - b_ref(k, j) *
a_ref(i__, k);
/* L80: */
}
}
/* L90: */
}
/* L100: */
}
}
} else {
/* Form B := alpha*inv( A' )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp = *alpha * b_ref(i__, j);
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
temp -= a_ref(k, i__) * b_ref(k, j);
/* L110: */
}
if (nounit) {
temp /= a_ref(i__, i__);
}
b_ref(i__, j) = temp;
/* L120: */
}
/* L130: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
temp = *alpha * b_ref(i__, j);
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
temp -= a_ref(k, i__) * b_ref(k, j);
/* L140: */
}
if (nounit) {
temp /= a_ref(i__, i__);
}
b_ref(i__, j) = temp;
/* L150: */
}
/* L160: */
}
}
}
} else {
if (template_blas_lsame(transa, "N")) {
/* Form B := alpha*B*inv( A ). */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (*alpha != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = *alpha * b_ref(i__, j);
/* L170: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
if (a_ref(k, j) != 0.) {
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b_ref(i__, j) = b_ref(i__, j) - a_ref(k, j) *
b_ref(i__, k);
/* L180: */
}
}
/* L190: */
}
if (nounit) {
temp = 1. / a_ref(j, j);
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = temp * b_ref(i__, j);
/* L200: */
}
}
/* L210: */
}
} else {
for (j = *n; j >= 1; --j) {
if (*alpha != 1.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b_ref(i__, j) = *alpha * b_ref(i__, j);
/* L220: */
}
}
i__1 = *n;
for (k = j + 1; k <= i__1; ++k) {
if (a_ref(k, j) != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = b_ref(i__, j) - a_ref(k, j) *
b_ref(i__, k);
/* L230: */
}
}
/* L240: */
}
if (nounit) {
temp = 1. / a_ref(j, j);
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b_ref(i__, j) = temp * b_ref(i__, j);
/* L250: */
}
}
/* L260: */
}
}
} else {
/* Form B := alpha*B*inv( A' ). */
if (upper) {
for (k = *n; k >= 1; --k) {
if (nounit) {
temp = 1. / a_ref(k, k);
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b_ref(i__, k) = temp * b_ref(i__, k);
/* L270: */
}
}
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
if (a_ref(j, k) != 0.) {
temp = a_ref(j, k);
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, j) = b_ref(i__, j) - temp * b_ref(
i__, k);
/* L280: */
}
}
/* L290: */
}
if (*alpha != 1.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
b_ref(i__, k) = *alpha * b_ref(i__, k);
/* L300: */
}
}
/* L310: */
}
} else {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (nounit) {
temp = 1. / a_ref(k, k);
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, k) = temp * b_ref(i__, k);
/* L320: */
}
}
i__2 = *n;
for (j = k + 1; j <= i__2; ++j) {
if (a_ref(j, k) != 0.) {
temp = a_ref(j, k);
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
b_ref(i__, j) = b_ref(i__, j) - temp * b_ref(
i__, k);
/* L330: */
}
}
/* L340: */
}
if (*alpha != 1.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
b_ref(i__, k) = *alpha * b_ref(i__, k);
/* L350: */
}
}
/* L360: */
}
}
}
}
return 0;
/* End of DTRSM . */
} /* dtrsm_ */
#undef b_ref
#undef a_ref
#endif
|
