1 /* ./src_f77/zlantr.f -- translated by f2c (version 20030320).
2 You must link the resulting object file with the libraries:
3 -lf2c -lm (in that order)
4 */
5
6 #include <punc/vf2c.h>
7
8 /* Table of constant values */
9
10 static integer c__1 = 1;
11
zlantr_(char * norm,char * uplo,char * diag,integer * m,integer * n,doublecomplex * a,integer * lda,doublereal * work,ftnlen norm_len,ftnlen uplo_len,ftnlen diag_len)12 doublereal zlantr_(char *norm, char *uplo, char *diag, integer *m, integer *n,
13 doublecomplex *a, integer *lda, doublereal *work, ftnlen norm_len,
14 ftnlen uplo_len, ftnlen diag_len)
15 {
16 /* System generated locals */
17 integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
18 doublereal ret_val, d__1, d__2;
19
20 /* Builtin functions */
21 double z_abs(doublecomplex *), sqrt(doublereal);
22
23 /* Local variables */
24 static integer i__, j;
25 static doublereal sum, scale;
26 static logical udiag;
27 extern logical lsame_(char *, char *, ftnlen, ftnlen);
28 static doublereal value;
29 extern /* Subroutine */ int zlassq_(integer *, doublecomplex *, integer *,
30 doublereal *, doublereal *);
31
32
33 /* -- LAPACK auxiliary routine (version 3.0) -- */
34 /* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
35 /* Courant Institute, Argonne National Lab, and Rice University */
36 /* October 31, 1992 */
37
38 /* .. Scalar Arguments .. */
39 /* .. */
40 /* .. Array Arguments .. */
41 /* .. */
42
43 /* Purpose */
44 /* ======= */
45
46 /* ZLANTR returns the value of the one norm, or the Frobenius norm, or */
47 /* the infinity norm, or the element of largest absolute value of a */
48 /* trapezoidal or triangular matrix A. */
49
50 /* Description */
51 /* =========== */
52
53 /* ZLANTR returns the value */
54
55 /* ZLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm' */
56 /* ( */
57 /* ( norm1(A), NORM = '1', 'O' or 'o' */
58 /* ( */
59 /* ( normI(A), NORM = 'I' or 'i' */
60 /* ( */
61 /* ( normF(A), NORM = 'F', 'f', 'E' or 'e' */
62
63 /* where norm1 denotes the one norm of a matrix (maximum column sum), */
64 /* normI denotes the infinity norm of a matrix (maximum row sum) and */
65 /* normF denotes the Frobenius norm of a matrix (square root of sum of */
66 /* squares). Note that max(abs(A(i,j))) is not a matrix norm. */
67
68 /* Arguments */
69 /* ========= */
70
71 /* NORM (input) CHARACTER*1 */
72 /* Specifies the value to be returned in ZLANTR as described */
73 /* above. */
74
75 /* UPLO (input) CHARACTER*1 */
76 /* Specifies whether the matrix A is upper or lower trapezoidal. */
77 /* = 'U': Upper trapezoidal */
78 /* = 'L': Lower trapezoidal */
79 /* Note that A is triangular instead of trapezoidal if M = N. */
80
81 /* DIAG (input) CHARACTER*1 */
82 /* Specifies whether or not the matrix A has unit diagonal. */
83 /* = 'N': Non-unit diagonal */
84 /* = 'U': Unit diagonal */
85
86 /* M (input) INTEGER */
87 /* The number of rows of the matrix A. M >= 0, and if */
88 /* UPLO = 'U', M <= N. When M = 0, ZLANTR is set to zero. */
89
90 /* N (input) INTEGER */
91 /* The number of columns of the matrix A. N >= 0, and if */
92 /* UPLO = 'L', N <= M. When N = 0, ZLANTR is set to zero. */
93
94 /* A (input) COMPLEX*16 array, dimension (LDA,N) */
95 /* The trapezoidal matrix A (A is triangular if M = N). */
96 /* If UPLO = 'U', the leading m by n upper trapezoidal part of */
97 /* the array A contains the upper trapezoidal matrix, and the */
98 /* strictly lower triangular part of A is not referenced. */
99 /* If UPLO = 'L', the leading m by n lower trapezoidal part of */
100 /* the array A contains the lower trapezoidal matrix, and the */
101 /* strictly upper triangular part of A is not referenced. Note */
102 /* that when DIAG = 'U', the diagonal elements of A are not */
103 /* referenced and are assumed to be one. */
104
105 /* LDA (input) INTEGER */
106 /* The leading dimension of the array A. LDA >= max(M,1). */
107
108 /* WORK (workspace) DOUBLE PRECISION array, dimension (LWORK), */
109 /* where LWORK >= M when NORM = 'I'; otherwise, WORK is not */
110 /* referenced. */
111
112 /* ===================================================================== */
113
114 /* .. Parameters .. */
115 /* .. */
116 /* .. Local Scalars .. */
117 /* .. */
118 /* .. External Functions .. */
119 /* .. */
120 /* .. External Subroutines .. */
121 /* .. */
122 /* .. Intrinsic Functions .. */
123 /* .. */
124 /* .. Executable Statements .. */
125
126 /* Parameter adjustments */
127 a_dim1 = *lda;
128 a_offset = 1 + a_dim1;
129 a -= a_offset;
130 --work;
131
132 /* Function Body */
133 if (min(*m,*n) == 0) {
134 value = 0.;
135 } else if (lsame_(norm, "M", (ftnlen)1, (ftnlen)1)) {
136
137 /* Find max(abs(A(i,j))). */
138
139 if (lsame_(diag, "U", (ftnlen)1, (ftnlen)1)) {
140 value = 1.;
141 if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
142 i__1 = *n;
143 for (j = 1; j <= i__1; ++j) {
144 /* Computing MIN */
145 i__3 = *m, i__4 = j - 1;
146 i__2 = min(i__3,i__4);
147 for (i__ = 1; i__ <= i__2; ++i__) {
148 /* Computing MAX */
149 d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
150 value = max(d__1,d__2);
151 /* L10: */
152 }
153 /* L20: */
154 }
155 } else {
156 i__1 = *n;
157 for (j = 1; j <= i__1; ++j) {
158 i__2 = *m;
159 for (i__ = j + 1; i__ <= i__2; ++i__) {
160 /* Computing MAX */
161 d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
162 value = max(d__1,d__2);
163 /* L30: */
164 }
165 /* L40: */
166 }
167 }
168 } else {
169 value = 0.;
170 if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
171 i__1 = *n;
172 for (j = 1; j <= i__1; ++j) {
173 i__2 = min(*m,j);
174 for (i__ = 1; i__ <= i__2; ++i__) {
175 /* Computing MAX */
176 d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
177 value = max(d__1,d__2);
178 /* L50: */
179 }
180 /* L60: */
181 }
182 } else {
183 i__1 = *n;
184 for (j = 1; j <= i__1; ++j) {
185 i__2 = *m;
186 for (i__ = j; i__ <= i__2; ++i__) {
187 /* Computing MAX */
188 d__1 = value, d__2 = z_abs(&a[i__ + j * a_dim1]);
189 value = max(d__1,d__2);
190 /* L70: */
191 }
192 /* L80: */
193 }
194 }
195 }
196 } else if (lsame_(norm, "O", (ftnlen)1, (ftnlen)1) || *(unsigned char *)
197 norm == '1') {
198
199 /* Find norm1(A). */
200
201 value = 0.;
202 udiag = lsame_(diag, "U", (ftnlen)1, (ftnlen)1);
203 if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
204 i__1 = *n;
205 for (j = 1; j <= i__1; ++j) {
206 if (udiag && j <= *m) {
207 sum = 1.;
208 i__2 = j - 1;
209 for (i__ = 1; i__ <= i__2; ++i__) {
210 sum += z_abs(&a[i__ + j * a_dim1]);
211 /* L90: */
212 }
213 } else {
214 sum = 0.;
215 i__2 = min(*m,j);
216 for (i__ = 1; i__ <= i__2; ++i__) {
217 sum += z_abs(&a[i__ + j * a_dim1]);
218 /* L100: */
219 }
220 }
221 value = max(value,sum);
222 /* L110: */
223 }
224 } else {
225 i__1 = *n;
226 for (j = 1; j <= i__1; ++j) {
227 if (udiag) {
228 sum = 1.;
229 i__2 = *m;
230 for (i__ = j + 1; i__ <= i__2; ++i__) {
231 sum += z_abs(&a[i__ + j * a_dim1]);
232 /* L120: */
233 }
234 } else {
235 sum = 0.;
236 i__2 = *m;
237 for (i__ = j; i__ <= i__2; ++i__) {
238 sum += z_abs(&a[i__ + j * a_dim1]);
239 /* L130: */
240 }
241 }
242 value = max(value,sum);
243 /* L140: */
244 }
245 }
246 } else if (lsame_(norm, "I", (ftnlen)1, (ftnlen)1)) {
247
248 /* Find normI(A). */
249
250 if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
251 if (lsame_(diag, "U", (ftnlen)1, (ftnlen)1)) {
252 i__1 = *m;
253 for (i__ = 1; i__ <= i__1; ++i__) {
254 work[i__] = 1.;
255 /* L150: */
256 }
257 i__1 = *n;
258 for (j = 1; j <= i__1; ++j) {
259 /* Computing MIN */
260 i__3 = *m, i__4 = j - 1;
261 i__2 = min(i__3,i__4);
262 for (i__ = 1; i__ <= i__2; ++i__) {
263 work[i__] += z_abs(&a[i__ + j * a_dim1]);
264 /* L160: */
265 }
266 /* L170: */
267 }
268 } else {
269 i__1 = *m;
270 for (i__ = 1; i__ <= i__1; ++i__) {
271 work[i__] = 0.;
272 /* L180: */
273 }
274 i__1 = *n;
275 for (j = 1; j <= i__1; ++j) {
276 i__2 = min(*m,j);
277 for (i__ = 1; i__ <= i__2; ++i__) {
278 work[i__] += z_abs(&a[i__ + j * a_dim1]);
279 /* L190: */
280 }
281 /* L200: */
282 }
283 }
284 } else {
285 if (lsame_(diag, "U", (ftnlen)1, (ftnlen)1)) {
286 i__1 = *n;
287 for (i__ = 1; i__ <= i__1; ++i__) {
288 work[i__] = 1.;
289 /* L210: */
290 }
291 i__1 = *m;
292 for (i__ = *n + 1; i__ <= i__1; ++i__) {
293 work[i__] = 0.;
294 /* L220: */
295 }
296 i__1 = *n;
297 for (j = 1; j <= i__1; ++j) {
298 i__2 = *m;
299 for (i__ = j + 1; i__ <= i__2; ++i__) {
300 work[i__] += z_abs(&a[i__ + j * a_dim1]);
301 /* L230: */
302 }
303 /* L240: */
304 }
305 } else {
306 i__1 = *m;
307 for (i__ = 1; i__ <= i__1; ++i__) {
308 work[i__] = 0.;
309 /* L250: */
310 }
311 i__1 = *n;
312 for (j = 1; j <= i__1; ++j) {
313 i__2 = *m;
314 for (i__ = j; i__ <= i__2; ++i__) {
315 work[i__] += z_abs(&a[i__ + j * a_dim1]);
316 /* L260: */
317 }
318 /* L270: */
319 }
320 }
321 }
322 value = 0.;
323 i__1 = *m;
324 for (i__ = 1; i__ <= i__1; ++i__) {
325 /* Computing MAX */
326 d__1 = value, d__2 = work[i__];
327 value = max(d__1,d__2);
328 /* L280: */
329 }
330 } else if (lsame_(norm, "F", (ftnlen)1, (ftnlen)1) || lsame_(norm, "E", (
331 ftnlen)1, (ftnlen)1)) {
332
333 /* Find normF(A). */
334
335 if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
336 if (lsame_(diag, "U", (ftnlen)1, (ftnlen)1)) {
337 scale = 1.;
338 sum = (doublereal) min(*m,*n);
339 i__1 = *n;
340 for (j = 2; j <= i__1; ++j) {
341 /* Computing MIN */
342 i__3 = *m, i__4 = j - 1;
343 i__2 = min(i__3,i__4);
344 zlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
345 /* L290: */
346 }
347 } else {
348 scale = 0.;
349 sum = 1.;
350 i__1 = *n;
351 for (j = 1; j <= i__1; ++j) {
352 i__2 = min(*m,j);
353 zlassq_(&i__2, &a[j * a_dim1 + 1], &c__1, &scale, &sum);
354 /* L300: */
355 }
356 }
357 } else {
358 if (lsame_(diag, "U", (ftnlen)1, (ftnlen)1)) {
359 scale = 1.;
360 sum = (doublereal) min(*m,*n);
361 i__1 = *n;
362 for (j = 1; j <= i__1; ++j) {
363 i__2 = *m - j;
364 /* Computing MIN */
365 i__3 = *m, i__4 = j + 1;
366 zlassq_(&i__2, &a[min(i__3,i__4) + j * a_dim1], &c__1, &
367 scale, &sum);
368 /* L310: */
369 }
370 } else {
371 scale = 0.;
372 sum = 1.;
373 i__1 = *n;
374 for (j = 1; j <= i__1; ++j) {
375 i__2 = *m - j + 1;
376 zlassq_(&i__2, &a[j + j * a_dim1], &c__1, &scale, &sum);
377 /* L320: */
378 }
379 }
380 }
381 value = scale * sqrt(sum);
382 }
383
384 ret_val = value;
385 return ret_val;
386
387 /* End of ZLANTR */
388
389 } /* zlantr_ */
390
391