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
|
/* ../blas/src/dsymm.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
/* Subroutine */ int REF_dsymm_(char *side, char *uplo, integer *m, integer *n,
doublereal *alpha, doublereal *a, integer *lda, doublereal *b,
integer *ldb, doublereal *beta, doublereal *c__, integer *ldc, ftnlen
side_len, ftnlen uplo_len)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, c_dim1, c_offset, i__1, i__2,
i__3;
/* Local variables */
static integer i__, j, k, info;
static doublereal temp1, temp2;
extern logical lsame_(char *, char *, ftnlen, ftnlen);
static integer nrowa;
static logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
/* .. Scalar Arguments .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DSYMM performs one of the matrix-matrix operations */
/* C := alpha*A*B + beta*C, */
/* or */
/* C := alpha*B*A + beta*C, */
/* where alpha and beta are scalars, A is a symmetric matrix and B and */
/* C are m by n matrices. */
/* Parameters */
/* ========== */
/* SIDE - CHARACTER*1. */
/* On entry, SIDE specifies whether the symmetric matrix A */
/* appears on the left or right in the operation as follows: */
/* SIDE = 'L' or 'l' C := alpha*A*B + beta*C, */
/* SIDE = 'R' or 'r' C := alpha*B*A + beta*C, */
/* Unchanged on exit. */
/* UPLO - CHARACTER*1. */
/* On entry, UPLO specifies whether the upper or lower */
/* triangular part of the symmetric matrix A is to be */
/* referenced as follows: */
/* UPLO = 'U' or 'u' Only the upper triangular part of the */
/* symmetric matrix is to be referenced. */
/* UPLO = 'L' or 'l' Only the lower triangular part of the */
/* symmetric matrix is to be referenced. */
/* Unchanged on exit. */
/* M - INTEGER. */
/* On entry, M specifies the number of rows of the matrix C. */
/* M must be at least zero. */
/* Unchanged on exit. */
/* N - INTEGER. */
/* On entry, N specifies the number of columns of the matrix C. */
/* N must be at least zero. */
/* Unchanged on exit. */
/* ALPHA - DOUBLE PRECISION. */
/* On entry, ALPHA specifies the scalar alpha. */
/* Unchanged on exit. */
/* A - DOUBLE PRECISION array of DIMENSION ( LDA, ka ), where ka is */
/* m when SIDE = 'L' or 'l' and is n otherwise. */
/* Before entry with SIDE = 'L' or 'l', the m by m part of */
/* the array A must contain the symmetric matrix, such that */
/* when UPLO = 'U' or 'u', the leading m by m upper triangular */
/* part of the array A must contain the upper triangular part */
/* of the symmetric matrix and the strictly lower triangular */
/* part of A is not referenced, and when UPLO = 'L' or 'l', */
/* the leading m by m lower triangular part of the array A */
/* must contain the lower triangular part of the symmetric */
/* matrix and the strictly upper triangular part of A is not */
/* referenced. */
/* Before entry with SIDE = 'R' or 'r', the n by n part of */
/* the array A must contain the symmetric matrix, such that */
/* when UPLO = 'U' or 'u', the leading n by n upper triangular */
/* part of the array A must contain the upper triangular part */
/* of the symmetric matrix and the strictly lower triangular */
/* part of A is not referenced, and when UPLO = 'L' or 'l', */
/* the leading n by n lower triangular part of the array A */
/* must contain the lower triangular part of the symmetric */
/* matrix and the strictly upper triangular part of A is not */
/* referenced. */
/* 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 ), otherwise 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 matrix B. */
/* Unchanged on exit. */
/* 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. */
/* BETA - DOUBLE PRECISION. */
/* On entry, BETA specifies the scalar beta. When BETA is */
/* supplied as zero then C need not be set on input. */
/* Unchanged on exit. */
/* C - DOUBLE PRECISION array of DIMENSION ( LDC, n ). */
/* Before entry, the leading m by n part of the array C must */
/* contain the matrix C, except when beta is zero, in which */
/* case C need not be set on entry. */
/* On exit, the array C is overwritten by the m by n updated */
/* matrix. */
/* LDC - INTEGER. */
/* On entry, LDC specifies the first dimension of C as declared */
/* in the calling (sub) program. LDC 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. */
/* .. External Functions .. */
/* .. External Subroutines .. */
/* .. Intrinsic Functions .. */
/* .. Local Scalars .. */
/* .. Parameters .. */
/* .. */
/* .. Executable Statements .. */
/* Set NROWA as the number of rows of A. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
/* Function Body */
if (lsame_(side, "L", (ftnlen)1, (ftnlen)1)) {
nrowa = *m;
} else {
nrowa = *n;
}
upper = lsame_(uplo, "U", (ftnlen)1, (ftnlen)1);
/* Test the input parameters. */
info = 0;
if (! lsame_(side, "L", (ftnlen)1, (ftnlen)1) && ! lsame_(side, "R", (
ftnlen)1, (ftnlen)1)) {
info = 1;
} else if (! upper && ! lsame_(uplo, "L", (ftnlen)1, (ftnlen)1)) {
info = 2;
} else if (*m < 0) {
info = 3;
} else if (*n < 0) {
info = 4;
} else if (*lda < max(1,nrowa)) {
info = 7;
} else if (*ldb < max(1,*m)) {
info = 9;
} else if (*ldc < max(1,*m)) {
info = 12;
}
if (info != 0) {
xerbla_("DSYMM ", &info, (ftnlen)6);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || *alpha == 0. && *beta == 1.) {
return 0;
}
/* And when alpha.eq.zero. */
if (*alpha == 0.) {
if (*beta == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = 0.;
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1];
/* L30: */
}
/* L40: */
}
}
return 0;
}
/* Start the operations. */
if (lsame_(side, "L", (ftnlen)1, (ftnlen)1)) {
/* Form C := alpha*A*B + beta*C. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
temp1 = *alpha * b[i__ + j * b_dim1];
temp2 = 0.;
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1];
temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1];
/* L50: */
}
if (*beta == 0.) {
c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1]
+ *alpha * temp2;
} else {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]
+ temp1 * a[i__ + i__ * a_dim1] + *alpha *
temp2;
}
/* L60: */
}
/* L70: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
temp1 = *alpha * b[i__ + j * b_dim1];
temp2 = 0.;
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
c__[k + j * c_dim1] += temp1 * a[k + i__ * a_dim1];
temp2 += b[k + j * b_dim1] * a[k + i__ * a_dim1];
/* L80: */
}
if (*beta == 0.) {
c__[i__ + j * c_dim1] = temp1 * a[i__ + i__ * a_dim1]
+ *alpha * temp2;
} else {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1]
+ temp1 * a[i__ + i__ * a_dim1] + *alpha *
temp2;
}
/* L90: */
}
/* L100: */
}
}
} else {
/* Form C := alpha*B*A + beta*C. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp1 = *alpha * a[j + j * a_dim1];
if (*beta == 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = temp1 * b[i__ + j * b_dim1];
/* L110: */
}
} else {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] = *beta * c__[i__ + j * c_dim1] +
temp1 * b[i__ + j * b_dim1];
/* L120: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
if (upper) {
temp1 = *alpha * a[k + j * a_dim1];
} else {
temp1 = *alpha * a[j + k * a_dim1];
}
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1];
/* L130: */
}
/* L140: */
}
i__2 = *n;
for (k = j + 1; k <= i__2; ++k) {
if (upper) {
temp1 = *alpha * a[j + k * a_dim1];
} else {
temp1 = *alpha * a[k + j * a_dim1];
}
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
c__[i__ + j * c_dim1] += temp1 * b[i__ + k * b_dim1];
/* L150: */
}
/* L160: */
}
/* L170: */
}
}
return 0;
/* End of DSYMM . */
} /* dsymm_ */
|
