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
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
|
/* zgbmv.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"
#include "blaswrap.h"
/* Subroutine */ int zgbmv_(char *trans, integer *m, integer *n, integer *kl,
integer *ku, doublecomplex *alpha, doublecomplex *a, integer *lda,
doublecomplex *x, integer *incx, doublecomplex *beta, doublecomplex *
y, integer *incy)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
doublecomplex z__1, z__2, z__3;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, j, k, ix, iy, jx, jy, kx, ky, kup1, info;
doublecomplex temp;
integer lenx, leny;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int xerbla_(char *, integer *);
logical noconj;
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZGBMV performs one of the matrix-vector operations */
/* y := alpha*A*x + beta*y, or y := alpha*A'*x + beta*y, or */
/* y := alpha*conjg( A' )*x + beta*y, */
/* where alpha and beta are scalars, x and y are vectors and A is an */
/* m by n band matrix, with kl sub-diagonals and ku super-diagonals. */
/* Arguments */
/* ========== */
/* TRANS - CHARACTER*1. */
/* On entry, TRANS specifies the operation to be performed as */
/* follows: */
/* TRANS = 'N' or 'n' y := alpha*A*x + beta*y. */
/* TRANS = 'T' or 't' y := alpha*A'*x + beta*y. */
/* TRANS = 'C' or 'c' y := alpha*conjg( A' )*x + beta*y. */
/* Unchanged on exit. */
/* M - INTEGER. */
/* On entry, M specifies the number of rows of the matrix A. */
/* M must be at least zero. */
/* Unchanged on exit. */
/* N - INTEGER. */
/* On entry, N specifies the number of columns of the matrix A. */
/* N must be at least zero. */
/* Unchanged on exit. */
/* KL - INTEGER. */
/* On entry, KL specifies the number of sub-diagonals of the */
/* matrix A. KL must satisfy 0 .le. KL. */
/* Unchanged on exit. */
/* KU - INTEGER. */
/* On entry, KU specifies the number of super-diagonals of the */
/* matrix A. KU must satisfy 0 .le. KU. */
/* Unchanged on exit. */
/* ALPHA - COMPLEX*16 . */
/* On entry, ALPHA specifies the scalar alpha. */
/* Unchanged on exit. */
/* A - COMPLEX*16 array of DIMENSION ( LDA, n ). */
/* Before entry, the leading ( kl + ku + 1 ) by n part of the */
/* array A must contain the matrix of coefficients, supplied */
/* column by column, with the leading diagonal of the matrix in */
/* row ( ku + 1 ) of the array, the first super-diagonal */
/* starting at position 2 in row ku, the first sub-diagonal */
/* starting at position 1 in row ( ku + 2 ), and so on. */
/* Elements in the array A that do not correspond to elements */
/* in the band matrix (such as the top left ku by ku triangle) */
/* are not referenced. */
/* The following program segment will transfer a band matrix */
/* from conventional full matrix storage to band storage: */
/* DO 20, J = 1, N */
/* K = KU + 1 - J */
/* DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL ) */
/* A( K + I, J ) = matrix( I, J ) */
/* 10 CONTINUE */
/* 20 CONTINUE */
/* Unchanged on exit. */
/* LDA - INTEGER. */
/* On entry, LDA specifies the first dimension of A as declared */
/* in the calling (sub) program. LDA must be at least */
/* ( kl + ku + 1 ). */
/* Unchanged on exit. */
/* X - COMPLEX*16 array of DIMENSION at least */
/* ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n' */
/* and at least */
/* ( 1 + ( m - 1 )*abs( INCX ) ) otherwise. */
/* Before entry, the incremented array X must contain the */
/* vector x. */
/* Unchanged on exit. */
/* INCX - INTEGER. */
/* On entry, INCX specifies the increment for the elements of */
/* X. INCX must not be zero. */
/* Unchanged on exit. */
/* BETA - COMPLEX*16 . */
/* On entry, BETA specifies the scalar beta. When BETA is */
/* supplied as zero then Y need not be set on input. */
/* Unchanged on exit. */
/* Y - COMPLEX*16 array of DIMENSION at least */
/* ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n' */
/* and at least */
/* ( 1 + ( n - 1 )*abs( INCY ) ) otherwise. */
/* Before entry, the incremented array Y must contain the */
/* vector y. On exit, Y is overwritten by the updated vector y. */
/* INCY - INTEGER. */
/* On entry, INCY specifies the increment for the elements of */
/* Y. INCY must not be zero. */
/* Unchanged on exit. */
/* Level 2 Blas routine. */
/* -- Written on 22-October-1986. */
/* Jack Dongarra, Argonne National Lab. */
/* Jeremy Du Croz, Nag Central Office. */
/* Sven Hammarling, Nag Central Office. */
/* Richard Hanson, Sandia National Labs. */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* Test the input parameters. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--x;
--y;
/* Function Body */
info = 0;
if (! lsame_(trans, "N") && ! lsame_(trans, "T") && ! lsame_(trans, "C")
) {
info = 1;
} else if (*m < 0) {
info = 2;
} else if (*n < 0) {
info = 3;
} else if (*kl < 0) {
info = 4;
} else if (*ku < 0) {
info = 5;
} else if (*lda < *kl + *ku + 1) {
info = 8;
} else if (*incx == 0) {
info = 10;
} else if (*incy == 0) {
info = 13;
}
if (info != 0) {
xerbla_("ZGBMV ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0 || alpha->r == 0. && alpha->i == 0. && (beta->r ==
1. && beta->i == 0.)) {
return 0;
}
noconj = lsame_(trans, "T");
/* Set LENX and LENY, the lengths of the vectors x and y, and set */
/* up the start points in X and Y. */
if (lsame_(trans, "N")) {
lenx = *n;
leny = *m;
} else {
lenx = *m;
leny = *n;
}
if (*incx > 0) {
kx = 1;
} else {
kx = 1 - (lenx - 1) * *incx;
}
if (*incy > 0) {
ky = 1;
} else {
ky = 1 - (leny - 1) * *incy;
}
/* Start the operations. In this version the elements of A are */
/* accessed sequentially with one pass through the band part of A. */
/* First form y := beta*y. */
if (beta->r != 1. || beta->i != 0.) {
if (*incy == 1) {
if (beta->r == 0. && beta->i == 0.) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
y[i__2].r = 0., y[i__2].i = 0.;
/* L10: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__;
i__3 = i__;
z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
.r;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
/* L20: */
}
}
} else {
iy = ky;
if (beta->r == 0. && beta->i == 0.) {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
y[i__2].r = 0., y[i__2].i = 0.;
iy += *incy;
/* L30: */
}
} else {
i__1 = leny;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = iy;
i__3 = iy;
z__1.r = beta->r * y[i__3].r - beta->i * y[i__3].i,
z__1.i = beta->r * y[i__3].i + beta->i * y[i__3]
.r;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
iy += *incy;
/* L40: */
}
}
}
}
if (alpha->r == 0. && alpha->i == 0.) {
return 0;
}
kup1 = *ku + 1;
if (lsame_(trans, "N")) {
/* Form y := alpha*A*x + y. */
jx = kx;
if (*incy == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = jx;
if (x[i__2].r != 0. || x[i__2].i != 0.) {
i__2 = jx;
z__1.r = alpha->r * x[i__2].r - alpha->i * x[i__2].i,
z__1.i = alpha->r * x[i__2].i + alpha->i * x[i__2]
.r;
temp.r = z__1.r, temp.i = z__1.i;
k = kup1 - j;
/* Computing MAX */
i__2 = 1, i__3 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__4 = min(i__5,i__6);
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
i__2 = i__;
i__3 = i__;
i__5 = k + i__ + j * a_dim1;
z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
z__2.i = temp.r * a[i__5].i + temp.i * a[i__5]
.r;
z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i +
z__2.i;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
/* L50: */
}
}
jx += *incx;
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__4 = jx;
if (x[i__4].r != 0. || x[i__4].i != 0.) {
i__4 = jx;
z__1.r = alpha->r * x[i__4].r - alpha->i * x[i__4].i,
z__1.i = alpha->r * x[i__4].i + alpha->i * x[i__4]
.r;
temp.r = z__1.r, temp.i = z__1.i;
iy = ky;
k = kup1 - j;
/* Computing MAX */
i__4 = 1, i__2 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__3 = min(i__5,i__6);
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
i__4 = iy;
i__2 = iy;
i__5 = k + i__ + j * a_dim1;
z__2.r = temp.r * a[i__5].r - temp.i * a[i__5].i,
z__2.i = temp.r * a[i__5].i + temp.i * a[i__5]
.r;
z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i +
z__2.i;
y[i__4].r = z__1.r, y[i__4].i = z__1.i;
iy += *incy;
/* L70: */
}
}
jx += *incx;
if (j > *ku) {
ky += *incy;
}
/* L80: */
}
}
} else {
/* Form y := alpha*A'*x + y or y := alpha*conjg( A' )*x + y. */
jy = ky;
if (*incx == 1) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp.r = 0., temp.i = 0.;
k = kup1 - j;
if (noconj) {
/* Computing MAX */
i__3 = 1, i__4 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__2 = min(i__5,i__6);
for (i__ = max(i__3,i__4); i__ <= i__2; ++i__) {
i__3 = k + i__ + j * a_dim1;
i__4 = i__;
z__2.r = a[i__3].r * x[i__4].r - a[i__3].i * x[i__4]
.i, z__2.i = a[i__3].r * x[i__4].i + a[i__3]
.i * x[i__4].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L90: */
}
} else {
/* Computing MAX */
i__2 = 1, i__3 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__4 = min(i__5,i__6);
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
d_cnjg(&z__3, &a[k + i__ + j * a_dim1]);
i__2 = i__;
z__2.r = z__3.r * x[i__2].r - z__3.i * x[i__2].i,
z__2.i = z__3.r * x[i__2].i + z__3.i * x[i__2]
.r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L100: */
}
}
i__4 = jy;
i__2 = jy;
z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i =
alpha->r * temp.i + alpha->i * temp.r;
z__1.r = y[i__2].r + z__2.r, z__1.i = y[i__2].i + z__2.i;
y[i__4].r = z__1.r, y[i__4].i = z__1.i;
jy += *incy;
/* L110: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
temp.r = 0., temp.i = 0.;
ix = kx;
k = kup1 - j;
if (noconj) {
/* Computing MAX */
i__4 = 1, i__2 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__3 = min(i__5,i__6);
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
i__4 = k + i__ + j * a_dim1;
i__2 = ix;
z__2.r = a[i__4].r * x[i__2].r - a[i__4].i * x[i__2]
.i, z__2.i = a[i__4].r * x[i__2].i + a[i__4]
.i * x[i__2].r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
ix += *incx;
/* L120: */
}
} else {
/* Computing MAX */
i__3 = 1, i__4 = j - *ku;
/* Computing MIN */
i__5 = *m, i__6 = j + *kl;
i__2 = min(i__5,i__6);
for (i__ = max(i__3,i__4); i__ <= i__2; ++i__) {
d_cnjg(&z__3, &a[k + i__ + j * a_dim1]);
i__3 = ix;
z__2.r = z__3.r * x[i__3].r - z__3.i * x[i__3].i,
z__2.i = z__3.r * x[i__3].i + z__3.i * x[i__3]
.r;
z__1.r = temp.r + z__2.r, z__1.i = temp.i + z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
ix += *incx;
/* L130: */
}
}
i__2 = jy;
i__3 = jy;
z__2.r = alpha->r * temp.r - alpha->i * temp.i, z__2.i =
alpha->r * temp.i + alpha->i * temp.r;
z__1.r = y[i__3].r + z__2.r, z__1.i = y[i__3].i + z__2.i;
y[i__2].r = z__1.r, y[i__2].i = z__1.i;
jy += *incy;
if (j > *ku) {
kx += *incx;
}
/* L140: */
}
}
}
return 0;
/* End of ZGBMV . */
} /* zgbmv_ */
|
