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
|
/* clantb.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"
/* Table of constant values */
static integer c__1 = 1;
doublereal clantb_(char *norm, char *uplo, char *diag, integer *n, integer *k,
complex *ab, integer *ldab, real *work)
{
/* System generated locals */
integer ab_dim1, ab_offset, i__1, i__2, i__3, i__4, i__5;
real ret_val, r__1, r__2;
/* Builtin functions */
double c_abs(complex *), sqrt(doublereal);
/* Local variables */
integer i__, j, l;
real sum, scale;
logical udiag;
extern logical lsame_(char *, char *);
real value;
extern /* Subroutine */ int classq_(integer *, complex *, integer *, real
*, real *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* CLANTB returns the value of the one norm, or the Frobenius norm, or */
/* the infinity norm, or the element of largest absolute value of an */
/* n by n triangular band matrix A, with ( k + 1 ) diagonals. */
/* Description */
/* =========== */
/* CLANTB returns the value */
/* CLANTB = ( max(abs(A(i,j))), NORM = 'M' or 'm' */
/* ( */
/* ( norm1(A), NORM = '1', 'O' or 'o' */
/* ( */
/* ( normI(A), NORM = 'I' or 'i' */
/* ( */
/* ( normF(A), NORM = 'F', 'f', 'E' or 'e' */
/* where norm1 denotes the one norm of a matrix (maximum column sum), */
/* normI denotes the infinity norm of a matrix (maximum row sum) and */
/* normF denotes the Frobenius norm of a matrix (square root of sum of */
/* squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. */
/* Arguments */
/* ========= */
/* NORM (input) CHARACTER*1 */
/* Specifies the value to be returned in CLANTB as described */
/* above. */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the matrix A is upper or lower triangular. */
/* = 'U': Upper triangular */
/* = 'L': Lower triangular */
/* DIAG (input) CHARACTER*1 */
/* Specifies whether or not the matrix A is unit triangular. */
/* = 'N': Non-unit triangular */
/* = 'U': Unit triangular */
/* N (input) INTEGER */
/* The order of the matrix A. N >= 0. When N = 0, CLANTB is */
/* set to zero. */
/* K (input) INTEGER */
/* The number of super-diagonals of the matrix A if UPLO = 'U', */
/* or the number of sub-diagonals of the matrix A if UPLO = 'L'. */
/* K >= 0. */
/* AB (input) COMPLEX array, dimension (LDAB,N) */
/* The upper or lower triangular band matrix A, stored in the */
/* first k+1 rows of AB. The j-th column of A is stored */
/* in the j-th column of the array AB as follows: */
/* if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; */
/* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). */
/* Note that when DIAG = 'U', the elements of the array AB */
/* corresponding to the diagonal elements of the matrix A are */
/* not referenced, but are assumed to be one. */
/* LDAB (input) INTEGER */
/* The leading dimension of the array AB. LDAB >= K+1. */
/* WORK (workspace) REAL array, dimension (MAX(1,LWORK)), */
/* where LWORK >= N when NORM = 'I'; otherwise, WORK is not */
/* referenced. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
ab_dim1 = *ldab;
ab_offset = 1 + ab_dim1;
ab -= ab_offset;
--work;
/* Function Body */
if (*n == 0) {
value = 0.f;
} else if (lsame_(norm, "M")) {
/* Find max(abs(A(i,j))). */
if (lsame_(diag, "U")) {
value = 1.f;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__2 = *k + 2 - j;
i__3 = *k;
for (i__ = max(i__2,1); i__ <= i__3; ++i__) {
/* Computing MAX */
r__1 = value, r__2 = c_abs(&ab[i__ + j * ab_dim1]);
value = dmax(r__1,r__2);
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__2 = *n + 1 - j, i__4 = *k + 1;
i__3 = min(i__2,i__4);
for (i__ = 2; i__ <= i__3; ++i__) {
/* Computing MAX */
r__1 = value, r__2 = c_abs(&ab[i__ + j * ab_dim1]);
value = dmax(r__1,r__2);
/* L30: */
}
/* L40: */
}
}
} else {
value = 0.f;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MAX */
i__3 = *k + 2 - j;
i__2 = *k + 1;
for (i__ = max(i__3,1); i__ <= i__2; ++i__) {
/* Computing MAX */
r__1 = value, r__2 = c_abs(&ab[i__ + j * ab_dim1]);
value = dmax(r__1,r__2);
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *n + 1 - j, i__4 = *k + 1;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
r__1 = value, r__2 = c_abs(&ab[i__ + j * ab_dim1]);
value = dmax(r__1,r__2);
/* L70: */
}
/* L80: */
}
}
}
} else if (lsame_(norm, "O") || *(unsigned char *)
norm == '1') {
/* Find norm1(A). */
value = 0.f;
udiag = lsame_(diag, "U");
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (udiag) {
sum = 1.f;
/* Computing MAX */
i__2 = *k + 2 - j;
i__3 = *k;
for (i__ = max(i__2,1); i__ <= i__3; ++i__) {
sum += c_abs(&ab[i__ + j * ab_dim1]);
/* L90: */
}
} else {
sum = 0.f;
/* Computing MAX */
i__3 = *k + 2 - j;
i__2 = *k + 1;
for (i__ = max(i__3,1); i__ <= i__2; ++i__) {
sum += c_abs(&ab[i__ + j * ab_dim1]);
/* L100: */
}
}
value = dmax(value,sum);
/* L110: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (udiag) {
sum = 1.f;
/* Computing MIN */
i__3 = *n + 1 - j, i__4 = *k + 1;
i__2 = min(i__3,i__4);
for (i__ = 2; i__ <= i__2; ++i__) {
sum += c_abs(&ab[i__ + j * ab_dim1]);
/* L120: */
}
} else {
sum = 0.f;
/* Computing MIN */
i__3 = *n + 1 - j, i__4 = *k + 1;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
sum += c_abs(&ab[i__ + j * ab_dim1]);
/* L130: */
}
}
value = dmax(value,sum);
/* L140: */
}
}
} else if (lsame_(norm, "I")) {
/* Find normI(A). */
value = 0.f;
if (lsame_(uplo, "U")) {
if (lsame_(diag, "U")) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 1.f;
/* L150: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = *k + 1 - j;
/* Computing MAX */
i__2 = 1, i__3 = j - *k;
i__4 = j - 1;
for (i__ = max(i__2,i__3); i__ <= i__4; ++i__) {
work[i__] += c_abs(&ab[l + i__ + j * ab_dim1]);
/* L160: */
}
/* L170: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.f;
/* L180: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = *k + 1 - j;
/* Computing MAX */
i__4 = 1, i__2 = j - *k;
i__3 = j;
for (i__ = max(i__4,i__2); i__ <= i__3; ++i__) {
work[i__] += c_abs(&ab[l + i__ + j * ab_dim1]);
/* L190: */
}
/* L200: */
}
}
} else {
if (lsame_(diag, "U")) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 1.f;
/* L210: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = 1 - j;
/* Computing MIN */
i__4 = *n, i__2 = j + *k;
i__3 = min(i__4,i__2);
for (i__ = j + 1; i__ <= i__3; ++i__) {
work[i__] += c_abs(&ab[l + i__ + j * ab_dim1]);
/* L220: */
}
/* L230: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.f;
/* L240: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
l = 1 - j;
/* Computing MIN */
i__4 = *n, i__2 = j + *k;
i__3 = min(i__4,i__2);
for (i__ = j; i__ <= i__3; ++i__) {
work[i__] += c_abs(&ab[l + i__ + j * ab_dim1]);
/* L250: */
}
/* L260: */
}
}
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
r__1 = value, r__2 = work[i__];
value = dmax(r__1,r__2);
/* L270: */
}
} else if (lsame_(norm, "F") || lsame_(norm, "E")) {
/* Find normF(A). */
if (lsame_(uplo, "U")) {
if (lsame_(diag, "U")) {
scale = 1.f;
sum = (real) (*n);
if (*k > 0) {
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
/* Computing MIN */
i__4 = j - 1;
i__3 = min(i__4,*k);
/* Computing MAX */
i__2 = *k + 2 - j;
classq_(&i__3, &ab[max(i__2, 1)+ j * ab_dim1], &c__1,
&scale, &sum);
/* L280: */
}
}
} else {
scale = 0.f;
sum = 1.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__4 = j, i__2 = *k + 1;
i__3 = min(i__4,i__2);
/* Computing MAX */
i__5 = *k + 2 - j;
classq_(&i__3, &ab[max(i__5, 1)+ j * ab_dim1], &c__1, &
scale, &sum);
/* L290: */
}
}
} else {
if (lsame_(diag, "U")) {
scale = 1.f;
sum = (real) (*n);
if (*k > 0) {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__4 = *n - j;
i__3 = min(i__4,*k);
classq_(&i__3, &ab[j * ab_dim1 + 2], &c__1, &scale, &
sum);
/* L300: */
}
}
} else {
scale = 0.f;
sum = 1.f;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__4 = *n - j + 1, i__2 = *k + 1;
i__3 = min(i__4,i__2);
classq_(&i__3, &ab[j * ab_dim1 + 1], &c__1, &scale, &sum);
/* L310: */
}
}
}
value = scale * sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of CLANTB */
} /* clantb_ */
|
