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
|
/* zlantr.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 zlantr_(char *norm, char *uplo, char *diag, integer *m, integer *n,
doublecomplex *a, integer *lda, doublereal *work)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
doublereal ret_val, d__1, d__2;
/* Builtin functions */
double z_abs(doublecomplex *), sqrt(doublereal);
/* Local variables */
integer i__, j;
doublereal sum, scale;
logical udiag;
extern logical lsame_(char *, char *);
doublereal value;
extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *,
doublereal *, doublereal *);
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZLANTR returns the value of the one norm, or the Frobenius norm, or */
/* the infinity norm, or the element of largest absolute value of a */
/* trapezoidal or triangular matrix A. */
/* Description */
/* =========== */
/* ZLANTR returns the value */
/* ZLANTR = ( 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 ZLANTR as described */
/* above. */
/* UPLO (input) CHARACTER*1 */
/* Specifies whether the matrix A is upper or lower trapezoidal. */
/* = 'U': Upper trapezoidal */
/* = 'L': Lower trapezoidal */
/* Note that A is triangular instead of trapezoidal if M = N. */
/* DIAG (input) CHARACTER*1 */
/* Specifies whether or not the matrix A has unit diagonal. */
/* = 'N': Non-unit diagonal */
/* = 'U': Unit diagonal */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0, and if */
/* UPLO = 'U', M <= N. When M = 0, ZLANTR is set to zero. */
/* N (input) INTEGER */
/* The number of columns of the matrix A. N >= 0, and if */
/* UPLO = 'L', N <= M. When N = 0, ZLANTR is set to zero. */
/* A (input) COMPLEX*16 array, dimension (LDA,N) */
/* The trapezoidal matrix A (A is triangular if M = N). */
/* If UPLO = 'U', the leading m by n upper trapezoidal part of */
/* the array A contains the upper trapezoidal matrix, and the */
/* strictly lower triangular part of A is not referenced. */
/* If UPLO = 'L', the leading m by n lower trapezoidal part of */
/* the array A contains the lower trapezoidal matrix, and the */
/* strictly upper triangular part of A is not referenced. Note */
/* that when DIAG = 'U', the diagonal elements of A are not */
/* referenced and are assumed to be one. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(M,1). */
/* WORK (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)), */
/* where LWORK >= M when NORM = 'I'; otherwise, WORK is not */
/* referenced. */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Intrinsic Functions .. */
/* .. */
/* .. Executable Statements .. */
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
--work;
/* Function Body */
if (min(*m,*n) == 0) {
value = 0.;
} else if (lsame_(norm, "M")) {
/* Find max(abs(A(i,j))). */
if (lsame_(diag, "U")) {
value = 1.;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *m, i__4 = j - 1;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
value = max(d__1,d__2);
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = j + 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
value = max(d__1,d__2);
/* L30: */
}
/* L40: */
}
}
} else {
value = 0.;
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = min(*m,j);
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
value = max(d__1,d__2);
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = j; i__ <= i__2; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
value = max(d__1,d__2);
/* L70: */
}
/* L80: */
}
}
}
} else if (lsame_(norm, "O") || *(unsigned char *)
norm == '1') {
/* Find norm1(A). */
value = 0.;
udiag = lsame_(diag, "U");
if (lsame_(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (udiag && j <= *m) {
sum = 1.;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
sum += z_abs(&a[i__ + j * a_dim1]);
/* L90: */
}
} else {
sum = 0.;
i__2 = min(*m,j);
for (i__ = 1; i__ <= i__2; ++i__) {
sum += z_abs(&a[i__ + j * a_dim1]);
/* L100: */
}
}
value = max(value,sum);
/* L110: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (udiag) {
sum = 1.;
i__2 = *m;
for (i__ = j + 1; i__ <= i__2; ++i__) {
sum += z_abs(&a[i__ + j * a_dim1]);
/* L120: */
}
} else {
sum = 0.;
i__2 = *m;
for (i__ = j; i__ <= i__2; ++i__) {
sum += z_abs(&a[i__ + j * a_dim1]);
/* L130: */
}
}
value = max(value,sum);
/* L140: */
}
}
} else if (lsame_(norm, "I")) {
/* Find normI(A). */
if (lsame_(uplo, "U")) {
if (lsame_(diag, "U")) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 1.;
/* L150: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *m, i__4 = j - 1;
i__2 = min(i__3,i__4);
for (i__ = 1; i__ <= i__2; ++i__) {
work[i__] += z_abs(&a[i__ + j * a_dim1]);
/* L160: */
}
/* L170: */
}
} else {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L180: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = min(*m,j);
for (i__ = 1; i__ <= i__2; ++i__) {
work[i__] += z_abs(&a[i__ + j * a_dim1]);
/* L190: */
}
/* L200: */
}
}
} else {
if (lsame_(diag, "U")) {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 1.;
/* L210: */
}
i__1 = *m;
for (i__ = *n + 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L220: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = j + 1; i__ <= i__2; ++i__) {
work[i__] += z_abs(&a[i__ + j * a_dim1]);
/* L230: */
}
/* L240: */
}
} else {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L250: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = j; i__ <= i__2; ++i__) {
work[i__] += z_abs(&a[i__ + j * a_dim1]);
/* L260: */
}
/* L270: */
}
}
}
value = 0.;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = work[i__];
value = max(d__1,d__2);
/* L280: */
}
} else if (lsame_(norm, "F") || lsame_(norm, "E")) {
/* Find normF(A). */
if (lsame_(uplo, "U")) {
if (lsame_(diag, "U")) {
scale = 1.;
sum = (doublereal) min(*m,*n);
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
/* Computing MIN */
i__3 = *m, i__4 = j - 1;
i__2 = min(i__3,i__4);
zlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
/* L290: */
}
} else {
scale = 0.;
sum = 1.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = min(*m,j);
zlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
/* L300: */
}
}
} else {
if (lsame_(diag, "U")) {
scale = 1.;
sum = (doublereal) min(*m,*n);
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m - j;
/* Computing MIN */
i__3 = *m, i__4 = j + 1;
zlassq_(&i__2, &a[min(i__3, i__4)+ j * a_dim1], &c__1, &
scale, &sum);
/* L310: */
}
} else {
scale = 0.;
sum = 1.;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m - j + 1;
zlassq_(&i__2, &a[j + j * a_dim1], &c__1, &scale, &sum);
/* L320: */
}
}
}
value = scale * sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of ZLANTR */
} /* zlantr_ */
|
