1 /* -- translated by f2c (version 20100827).
2 You must link the resulting object file with libf2c:
3 on Microsoft Windows system, link with libf2c.lib;
4 on Linux or Unix systems, link with .../path/to/libf2c.a -lm
5 or, if you install libf2c.a in a standard place, with -lf2c -lm
6 -- in that order, at the end of the command line, as in
7 cc *.o -lf2c -lm
8 Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
9
10 http://www.netlib.org/f2c/libf2c.zip
11 */
12
13 #include "f2c.h"
14
15 /* Table of constant values */
16
17 static doublecomplex c_b1 = {1.,0.};
18 static blasint c__1 = 1;
19
20 /** ZSYTRF_REC2 computes a partial factorization of a complex symmetric matrix using the Bunch-Kaufman diagon al pivoting method.
21 *
22 * This routine is a minor modification of LAPACK's zlasyf.
23 * It serves as an unblocked kernel in the recursive algorithms.
24 * The blocked BLAS Level 3 updates were removed and moved to the
25 * recursive algorithm.
26 * */
RELAPACK_zsytrf_rec2(char * uplo,blasint * n,blasint * nb,blasint * kb,doublecomplex * a,blasint * lda,blasint * ipiv,doublecomplex * w,blasint * ldw,blasint * info,ftnlen uplo_len)27 /* Subroutine */ void RELAPACK_zsytrf_rec2(char *uplo, blasint *n, blasint *
28 nb, blasint *kb, doublecomplex *a, blasint *lda, blasint *ipiv,
29 doublecomplex *w, blasint *ldw, blasint *info, ftnlen uplo_len)
30 {
31 /* System generated locals */
32 blasint a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4;
33 double d__1, d__2, d__3, d__4;
34 doublecomplex z__1, z__2, z__3;
35
36 /* Builtin functions */
37 double sqrt(double), d_imag(doublecomplex *);
38 void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
39
40 /* Local variables */
41 static blasint j, k;
42 static doublecomplex t, r1, d11, d21, d22;
43 static blasint jj, kk, jp, kp, kw, kkw, imax, jmax;
44 static double alpha;
45 extern logical lsame_(char *, char *, ftnlen, ftnlen);
46 extern /* Subroutine */ blasint zscal_(int *, doublecomplex *,
47 doublecomplex *, blasint *);
48 static blasint kstep;
49 extern /* Subroutine */ blasint zgemv_(char *, blasint *, blasint *,
50 doublecomplex *, doublecomplex *, blasint *, doublecomplex *,
51 blasint *, doublecomplex *, doublecomplex *, blasint *, ftnlen),
52 zcopy_(int *, doublecomplex *, blasint *, doublecomplex *,
53 blasint *), zswap_(int *, doublecomplex *, blasint *,
54 doublecomplex *, blasint *);
55 static double absakk, colmax;
56 extern blasint izamax_(int *, doublecomplex *, blasint *);
57 static double rowmax;
58
59 /* Parameter adjustments */
60 a_dim1 = *lda;
61 a_offset = 1 + a_dim1;
62 a -= a_offset;
63 --ipiv;
64 w_dim1 = *ldw;
65 w_offset = 1 + w_dim1;
66 w -= w_offset;
67
68 /* Function Body */
69 *info = 0;
70 alpha = (sqrt(17.) + 1.) / 8.;
71 if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) {
72 k = *n;
73 L10:
74 kw = *nb + k - *n;
75 if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) {
76 goto L30;
77 }
78 zcopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1);
79 if (k < *n) {
80 i__1 = *n - k;
81 z__1.r = -1., z__1.i = -0.;
82 zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) * a_dim1 + 1],
83 lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw *
84 w_dim1 + 1], &c__1, (ftnlen)12);
85 }
86 kstep = 1;
87 i__1 = k + kw * w_dim1;
88 absakk = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[k + kw *
89 w_dim1]), abs(d__2));
90 if (k > 1) {
91 i__1 = k - 1;
92 imax = izamax_(&i__1, &w[kw * w_dim1 + 1], &c__1);
93 i__1 = imax + kw * w_dim1;
94 colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
95 kw * w_dim1]), abs(d__2));
96 } else {
97 colmax = 0.;
98 }
99 if (max(absakk,colmax) == 0.) {
100 if (*info == 0) {
101 *info = k;
102 }
103 kp = k;
104 } else {
105 if (absakk >= alpha * colmax) {
106 kp = k;
107 } else {
108 zcopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) *
109 w_dim1 + 1], &c__1);
110 i__1 = k - imax;
111 zcopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax +
112 1 + (kw - 1) * w_dim1], &c__1);
113 if (k < *n) {
114 i__1 = *n - k;
115 z__1.r = -1., z__1.i = -0.;
116 zgemv_("No transpose", &k, &i__1, &z__1, &a[(k + 1) *
117 a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1],
118 ldw, &c_b1, &w[(kw - 1) * w_dim1 + 1], &c__1, (
119 ftnlen)12);
120 }
121 i__1 = k - imax;
122 jmax = imax + izamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1],
123 &c__1);
124 i__1 = jmax + (kw - 1) * w_dim1;
125 rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
126 jmax + (kw - 1) * w_dim1]), abs(d__2));
127 if (imax > 1) {
128 i__1 = imax - 1;
129 jmax = izamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1);
130 /* Computing MAX */
131 i__1 = jmax + (kw - 1) * w_dim1;
132 d__3 = rowmax, d__4 = (d__1 = w[i__1].r, abs(d__1)) + (
133 d__2 = d_imag(&w[jmax + (kw - 1) * w_dim1]), abs(
134 d__2));
135 rowmax = max(d__3,d__4);
136 }
137 if (absakk >= alpha * colmax * (colmax / rowmax)) {
138 kp = k;
139 } else /* if(complicated condition) */ {
140 i__1 = imax + (kw - 1) * w_dim1;
141 if ((d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
142 imax + (kw - 1) * w_dim1]), abs(d__2)) >= alpha *
143 rowmax) {
144 kp = imax;
145 zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw *
146 w_dim1 + 1], &c__1);
147 } else {
148 kp = imax;
149 kstep = 2;
150 }
151 }
152 }
153 kk = k - kstep + 1;
154 kkw = *nb + kk - *n;
155 if (kp != kk) {
156 i__1 = kp + kp * a_dim1;
157 i__2 = kk + kk * a_dim1;
158 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
159 i__1 = kk - 1 - kp;
160 zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp +
161 1) * a_dim1], lda);
162 if (kp > 1) {
163 i__1 = kp - 1;
164 zcopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1
165 + 1], &c__1);
166 }
167 if (k < *n) {
168 i__1 = *n - k;
169 zswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k
170 + 1) * a_dim1], lda);
171 }
172 i__1 = *n - kk + 1;
173 zswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw *
174 w_dim1], ldw);
175 }
176 if (kstep == 1) {
177 zcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &
178 c__1);
179 z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
180 r1.r = z__1.r, r1.i = z__1.i;
181 i__1 = k - 1;
182 zscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
183 } else {
184 if (k > 2) {
185 i__1 = k - 1 + kw * w_dim1;
186 d21.r = w[i__1].r, d21.i = w[i__1].i;
187 z_div(&z__1, &w[k + kw * w_dim1], &d21);
188 d11.r = z__1.r, d11.i = z__1.i;
189 z_div(&z__1, &w[k - 1 + (kw - 1) * w_dim1], &d21);
190 d22.r = z__1.r, d22.i = z__1.i;
191 z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r *
192 d22.i + d11.i * d22.r;
193 z__2.r = z__3.r - 1., z__2.i = z__3.i - 0.;
194 z_div(&z__1, &c_b1, &z__2);
195 t.r = z__1.r, t.i = z__1.i;
196 z_div(&z__1, &t, &d21);
197 d21.r = z__1.r, d21.i = z__1.i;
198 i__1 = k - 2;
199 for (j = 1; j <= i__1; ++j) {
200 i__2 = j + (k - 1) * a_dim1;
201 i__3 = j + (kw - 1) * w_dim1;
202 z__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
203 z__3.i = d11.r * w[i__3].i + d11.i * w[i__3]
204 .r;
205 i__4 = j + kw * w_dim1;
206 z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4]
207 .i;
208 z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
209 d21.r * z__2.i + d21.i * z__2.r;
210 a[i__2].r = z__1.r, a[i__2].i = z__1.i;
211 i__2 = j + k * a_dim1;
212 i__3 = j + kw * w_dim1;
213 z__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
214 z__3.i = d22.r * w[i__3].i + d22.i * w[i__3]
215 .r;
216 i__4 = j + (kw - 1) * w_dim1;
217 z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4]
218 .i;
219 z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
220 d21.r * z__2.i + d21.i * z__2.r;
221 a[i__2].r = z__1.r, a[i__2].i = z__1.i;
222 /* L20: */
223 }
224 }
225 i__1 = k - 1 + (k - 1) * a_dim1;
226 i__2 = k - 1 + (kw - 1) * w_dim1;
227 a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
228 i__1 = k - 1 + k * a_dim1;
229 i__2 = k - 1 + kw * w_dim1;
230 a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
231 i__1 = k + k * a_dim1;
232 i__2 = k + kw * w_dim1;
233 a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
234 }
235 }
236 if (kstep == 1) {
237 ipiv[k] = kp;
238 } else {
239 ipiv[k] = -kp;
240 ipiv[k - 1] = -kp;
241 }
242 k -= kstep;
243 goto L10;
244 L30:
245 j = k + 1;
246 L60:
247 jj = j;
248 jp = ipiv[j];
249 if (jp < 0) {
250 jp = -jp;
251 ++j;
252 }
253 ++j;
254 if (jp != jj && j <= *n) {
255 i__1 = *n - j + 1;
256 zswap_(&i__1, &a[jp + j * a_dim1], lda, &a[jj + j * a_dim1], lda);
257 }
258 if (j < *n) {
259 goto L60;
260 }
261 *kb = *n - k;
262 } else {
263 k = 1;
264 L70:
265 if ((k >= *nb && *nb < *n) || k > *n) {
266 goto L90;
267 }
268 i__1 = *n - k + 1;
269 zcopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1);
270 i__1 = *n - k + 1;
271 i__2 = k - 1;
272 z__1.r = -1., z__1.i = -0.;
273 zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1], lda, &w[k
274 + w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, (ftnlen)12);
275 kstep = 1;
276 i__1 = k + k * w_dim1;
277 absakk = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[k + k *
278 w_dim1]), abs(d__2));
279 if (k < *n) {
280 i__1 = *n - k;
281 imax = k + izamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1);
282 i__1 = imax + k * w_dim1;
283 colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[imax +
284 k * w_dim1]), abs(d__2));
285 } else {
286 colmax = 0.;
287 }
288 if (max(absakk,colmax) == 0.) {
289 if (*info == 0) {
290 *info = k;
291 }
292 kp = k;
293 } else {
294 if (absakk >= alpha * colmax) {
295 kp = k;
296 } else {
297 i__1 = imax - k;
298 zcopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) *
299 w_dim1], &c__1);
300 i__1 = *n - imax + 1;
301 zcopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k +
302 1) * w_dim1], &c__1);
303 i__1 = *n - k + 1;
304 i__2 = k - 1;
305 z__1.r = -1., z__1.i = -0.;
306 zgemv_("No transpose", &i__1, &i__2, &z__1, &a[k + a_dim1],
307 lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k + 1) *
308 w_dim1], &c__1, (ftnlen)12);
309 i__1 = imax - k;
310 jmax = k - 1 + izamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1)
311 ;
312 i__1 = jmax + (k + 1) * w_dim1;
313 rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
314 jmax + (k + 1) * w_dim1]), abs(d__2));
315 if (imax < *n) {
316 i__1 = *n - imax;
317 jmax = imax + izamax_(&i__1, &w[imax + 1 + (k + 1) *
318 w_dim1], &c__1);
319 /* Computing MAX */
320 i__1 = jmax + (k + 1) * w_dim1;
321 d__3 = rowmax, d__4 = (d__1 = w[i__1].r, abs(d__1)) + (
322 d__2 = d_imag(&w[jmax + (k + 1) * w_dim1]), abs(
323 d__2));
324 rowmax = max(d__3,d__4);
325 }
326 if (absakk >= alpha * colmax * (colmax / rowmax)) {
327 kp = k;
328 } else /* if(complicated condition) */ {
329 i__1 = imax + (k + 1) * w_dim1;
330 if ((d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_imag(&w[
331 imax + (k + 1) * w_dim1]), abs(d__2)) >= alpha *
332 rowmax) {
333 kp = imax;
334 i__1 = *n - k + 1;
335 zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k +
336 k * w_dim1], &c__1);
337 } else {
338 kp = imax;
339 kstep = 2;
340 }
341 }
342 }
343 kk = k + kstep - 1;
344 if (kp != kk) {
345 i__1 = kp + kp * a_dim1;
346 i__2 = kk + kk * a_dim1;
347 a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
348 i__1 = kp - kk - 1;
349 zcopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk +
350 1) * a_dim1], lda);
351 if (kp < *n) {
352 i__1 = *n - kp;
353 zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1
354 + kp * a_dim1], &c__1);
355 }
356 if (k > 1) {
357 i__1 = k - 1;
358 zswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda);
359 }
360 zswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw);
361 }
362 if (kstep == 1) {
363 i__1 = *n - k + 1;
364 zcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &
365 c__1);
366 if (k < *n) {
367 z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
368 r1.r = z__1.r, r1.i = z__1.i;
369 i__1 = *n - k;
370 zscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
371 }
372 } else {
373 if (k < *n - 1) {
374 i__1 = k + 1 + k * w_dim1;
375 d21.r = w[i__1].r, d21.i = w[i__1].i;
376 z_div(&z__1, &w[k + 1 + (k + 1) * w_dim1], &d21);
377 d11.r = z__1.r, d11.i = z__1.i;
378 z_div(&z__1, &w[k + k * w_dim1], &d21);
379 d22.r = z__1.r, d22.i = z__1.i;
380 z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r *
381 d22.i + d11.i * d22.r;
382 z__2.r = z__3.r - 1., z__2.i = z__3.i - 0.;
383 z_div(&z__1, &c_b1, &z__2);
384 t.r = z__1.r, t.i = z__1.i;
385 z_div(&z__1, &t, &d21);
386 d21.r = z__1.r, d21.i = z__1.i;
387 i__1 = *n;
388 for (j = k + 2; j <= i__1; ++j) {
389 i__2 = j + k * a_dim1;
390 i__3 = j + k * w_dim1;
391 z__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i,
392 z__3.i = d11.r * w[i__3].i + d11.i * w[i__3]
393 .r;
394 i__4 = j + (k + 1) * w_dim1;
395 z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4]
396 .i;
397 z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
398 d21.r * z__2.i + d21.i * z__2.r;
399 a[i__2].r = z__1.r, a[i__2].i = z__1.i;
400 i__2 = j + (k + 1) * a_dim1;
401 i__3 = j + (k + 1) * w_dim1;
402 z__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i,
403 z__3.i = d22.r * w[i__3].i + d22.i * w[i__3]
404 .r;
405 i__4 = j + k * w_dim1;
406 z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4]
407 .i;
408 z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i =
409 d21.r * z__2.i + d21.i * z__2.r;
410 a[i__2].r = z__1.r, a[i__2].i = z__1.i;
411 /* L80: */
412 }
413 }
414 i__1 = k + k * a_dim1;
415 i__2 = k + k * w_dim1;
416 a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
417 i__1 = k + 1 + k * a_dim1;
418 i__2 = k + 1 + k * w_dim1;
419 a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
420 i__1 = k + 1 + (k + 1) * a_dim1;
421 i__2 = k + 1 + (k + 1) * w_dim1;
422 a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i;
423 }
424 }
425 if (kstep == 1) {
426 ipiv[k] = kp;
427 } else {
428 ipiv[k] = -kp;
429 ipiv[k + 1] = -kp;
430 }
431 k += kstep;
432 goto L70;
433 L90:
434 j = k - 1;
435 L120:
436 jj = j;
437 jp = ipiv[j];
438 if (jp < 0) {
439 jp = -jp;
440 --j;
441 }
442 --j;
443 if (jp != jj && j >= 1) {
444 zswap_(&j, &a[jp + a_dim1], lda, &a[jj + a_dim1], lda);
445 }
446 if (j > 1) {
447 goto L120;
448 }
449 *kb = k - 1;
450 }
451 return;
452 }
453