/src/igraph/vendor/lapack/dtrexc.c
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1 | | /* -- translated by f2c (version 20191129). |
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 integer c__1 = 1; |
18 | | static integer c__2 = 2; |
19 | | |
20 | | /* > \brief \b DTREXC |
21 | | |
22 | | =========== DOCUMENTATION =========== |
23 | | |
24 | | Online html documentation available at |
25 | | http://www.netlib.org/lapack/explore-html/ |
26 | | |
27 | | > \htmlonly |
28 | | > Download DTREXC + dependencies |
29 | | > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrexc. |
30 | | f"> |
31 | | > [TGZ]</a> |
32 | | > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtrexc. |
33 | | f"> |
34 | | > [ZIP]</a> |
35 | | > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtrexc. |
36 | | f"> |
37 | | > [TXT]</a> |
38 | | > \endhtmlonly |
39 | | |
40 | | Definition: |
41 | | =========== |
42 | | |
43 | | SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, |
44 | | INFO ) |
45 | | |
46 | | CHARACTER COMPQ |
47 | | INTEGER IFST, ILST, INFO, LDQ, LDT, N |
48 | | DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * ) |
49 | | |
50 | | |
51 | | > \par Purpose: |
52 | | ============= |
53 | | > |
54 | | > \verbatim |
55 | | > |
56 | | > DTREXC reorders the real Schur factorization of a real matrix |
57 | | > A = Q*T*Q**T, so that the diagonal block of T with row index IFST is |
58 | | > moved to row ILST. |
59 | | > |
60 | | > The real Schur form T is reordered by an orthogonal similarity |
61 | | > transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors |
62 | | > is updated by postmultiplying it with Z. |
63 | | > |
64 | | > T must be in Schur canonical form (as returned by DHSEQR), that is, |
65 | | > block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each |
66 | | > 2-by-2 diagonal block has its diagonal elements equal and its |
67 | | > off-diagonal elements of opposite sign. |
68 | | > \endverbatim |
69 | | |
70 | | Arguments: |
71 | | ========== |
72 | | |
73 | | > \param[in] COMPQ |
74 | | > \verbatim |
75 | | > COMPQ is CHARACTER*1 |
76 | | > = 'V': update the matrix Q of Schur vectors; |
77 | | > = 'N': do not update Q. |
78 | | > \endverbatim |
79 | | > |
80 | | > \param[in] N |
81 | | > \verbatim |
82 | | > N is INTEGER |
83 | | > The order of the matrix T. N >= 0. |
84 | | > \endverbatim |
85 | | > |
86 | | > \param[in,out] T |
87 | | > \verbatim |
88 | | > T is DOUBLE PRECISION array, dimension (LDT,N) |
89 | | > On entry, the upper quasi-triangular matrix T, in Schur |
90 | | > Schur canonical form. |
91 | | > On exit, the reordered upper quasi-triangular matrix, again |
92 | | > in Schur canonical form. |
93 | | > \endverbatim |
94 | | > |
95 | | > \param[in] LDT |
96 | | > \verbatim |
97 | | > LDT is INTEGER |
98 | | > The leading dimension of the array T. LDT >= max(1,N). |
99 | | > \endverbatim |
100 | | > |
101 | | > \param[in,out] Q |
102 | | > \verbatim |
103 | | > Q is DOUBLE PRECISION array, dimension (LDQ,N) |
104 | | > On entry, if COMPQ = 'V', the matrix Q of Schur vectors. |
105 | | > On exit, if COMPQ = 'V', Q has been postmultiplied by the |
106 | | > orthogonal transformation matrix Z which reorders T. |
107 | | > If COMPQ = 'N', Q is not referenced. |
108 | | > \endverbatim |
109 | | > |
110 | | > \param[in] LDQ |
111 | | > \verbatim |
112 | | > LDQ is INTEGER |
113 | | > The leading dimension of the array Q. LDQ >= max(1,N). |
114 | | > \endverbatim |
115 | | > |
116 | | > \param[in,out] IFST |
117 | | > \verbatim |
118 | | > IFST is INTEGER |
119 | | > \endverbatim |
120 | | > |
121 | | > \param[in,out] ILST |
122 | | > \verbatim |
123 | | > ILST is INTEGER |
124 | | > |
125 | | > Specify the reordering of the diagonal blocks of T. |
126 | | > The block with row index IFST is moved to row ILST, by a |
127 | | > sequence of transpositions between adjacent blocks. |
128 | | > On exit, if IFST pointed on entry to the second row of a |
129 | | > 2-by-2 block, it is changed to point to the first row; ILST |
130 | | > always points to the first row of the block in its final |
131 | | > position (which may differ from its input value by +1 or -1). |
132 | | > 1 <= IFST <= N; 1 <= ILST <= N. |
133 | | > \endverbatim |
134 | | > |
135 | | > \param[out] WORK |
136 | | > \verbatim |
137 | | > WORK is DOUBLE PRECISION array, dimension (N) |
138 | | > \endverbatim |
139 | | > |
140 | | > \param[out] INFO |
141 | | > \verbatim |
142 | | > INFO is INTEGER |
143 | | > = 0: successful exit |
144 | | > < 0: if INFO = -i, the i-th argument had an illegal value |
145 | | > = 1: two adjacent blocks were too close to swap (the problem |
146 | | > is very ill-conditioned); T may have been partially |
147 | | > reordered, and ILST points to the first row of the |
148 | | > current position of the block being moved. |
149 | | > \endverbatim |
150 | | |
151 | | Authors: |
152 | | ======== |
153 | | |
154 | | > \author Univ. of Tennessee |
155 | | > \author Univ. of California Berkeley |
156 | | > \author Univ. of Colorado Denver |
157 | | > \author NAG Ltd. |
158 | | |
159 | | > \date November 2011 |
160 | | |
161 | | > \ingroup doubleOTHERcomputational |
162 | | |
163 | | ===================================================================== |
164 | | Subroutine */ int igraphdtrexc_(char *compq, integer *n, doublereal *t, integer * |
165 | | ldt, doublereal *q, integer *ldq, integer *ifst, integer *ilst, |
166 | | doublereal *work, integer *info) |
167 | 0 | { |
168 | | /* System generated locals */ |
169 | 0 | integer q_dim1, q_offset, t_dim1, t_offset, i__1; |
170 | | |
171 | | /* Local variables */ |
172 | 0 | integer nbf, nbl, here; |
173 | 0 | extern logical igraphlsame_(char *, char *); |
174 | 0 | logical wantq; |
175 | 0 | extern /* Subroutine */ int igraphdlaexc_(logical *, integer *, doublereal *, |
176 | 0 | integer *, doublereal *, integer *, integer *, integer *, integer |
177 | 0 | *, doublereal *, integer *), igraphxerbla_(char *, integer *, ftnlen); |
178 | 0 | integer nbnext; |
179 | | |
180 | | |
181 | | /* -- LAPACK computational routine (version 3.4.0) -- |
182 | | -- LAPACK is a software package provided by Univ. of Tennessee, -- |
183 | | -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
184 | | November 2011 |
185 | | |
186 | | |
187 | | ===================================================================== |
188 | | |
189 | | |
190 | | Decode and test the input arguments. |
191 | | |
192 | | Parameter adjustments */ |
193 | 0 | t_dim1 = *ldt; |
194 | 0 | t_offset = 1 + t_dim1; |
195 | 0 | t -= t_offset; |
196 | 0 | q_dim1 = *ldq; |
197 | 0 | q_offset = 1 + q_dim1; |
198 | 0 | q -= q_offset; |
199 | 0 | --work; |
200 | | |
201 | | /* Function Body */ |
202 | 0 | *info = 0; |
203 | 0 | wantq = igraphlsame_(compq, "V"); |
204 | 0 | if (! wantq && ! igraphlsame_(compq, "N")) { |
205 | 0 | *info = -1; |
206 | 0 | } else if (*n < 0) { |
207 | 0 | *info = -2; |
208 | 0 | } else if (*ldt < max(1,*n)) { |
209 | 0 | *info = -4; |
210 | 0 | } else if (*ldq < 1 || wantq && *ldq < max(1,*n)) { |
211 | 0 | *info = -6; |
212 | 0 | } else if (*ifst < 1 || *ifst > *n) { |
213 | 0 | *info = -7; |
214 | 0 | } else if (*ilst < 1 || *ilst > *n) { |
215 | 0 | *info = -8; |
216 | 0 | } |
217 | 0 | if (*info != 0) { |
218 | 0 | i__1 = -(*info); |
219 | 0 | igraphxerbla_("DTREXC", &i__1, (ftnlen)6); |
220 | 0 | return 0; |
221 | 0 | } |
222 | | |
223 | | /* Quick return if possible */ |
224 | | |
225 | 0 | if (*n <= 1) { |
226 | 0 | return 0; |
227 | 0 | } |
228 | | |
229 | | /* Determine the first row of specified block |
230 | | and find out it is 1 by 1 or 2 by 2. */ |
231 | | |
232 | 0 | if (*ifst > 1) { |
233 | 0 | if (t[*ifst + (*ifst - 1) * t_dim1] != 0.) { |
234 | 0 | --(*ifst); |
235 | 0 | } |
236 | 0 | } |
237 | 0 | nbf = 1; |
238 | 0 | if (*ifst < *n) { |
239 | 0 | if (t[*ifst + 1 + *ifst * t_dim1] != 0.) { |
240 | 0 | nbf = 2; |
241 | 0 | } |
242 | 0 | } |
243 | | |
244 | | /* Determine the first row of the final block |
245 | | and find out it is 1 by 1 or 2 by 2. */ |
246 | |
|
247 | 0 | if (*ilst > 1) { |
248 | 0 | if (t[*ilst + (*ilst - 1) * t_dim1] != 0.) { |
249 | 0 | --(*ilst); |
250 | 0 | } |
251 | 0 | } |
252 | 0 | nbl = 1; |
253 | 0 | if (*ilst < *n) { |
254 | 0 | if (t[*ilst + 1 + *ilst * t_dim1] != 0.) { |
255 | 0 | nbl = 2; |
256 | 0 | } |
257 | 0 | } |
258 | |
|
259 | 0 | if (*ifst == *ilst) { |
260 | 0 | return 0; |
261 | 0 | } |
262 | | |
263 | 0 | if (*ifst < *ilst) { |
264 | | |
265 | | /* Update ILST */ |
266 | |
|
267 | 0 | if (nbf == 2 && nbl == 1) { |
268 | 0 | --(*ilst); |
269 | 0 | } |
270 | 0 | if (nbf == 1 && nbl == 2) { |
271 | 0 | ++(*ilst); |
272 | 0 | } |
273 | |
|
274 | 0 | here = *ifst; |
275 | |
|
276 | 0 | L10: |
277 | | |
278 | | /* Swap block with next one below */ |
279 | |
|
280 | 0 | if (nbf == 1 || nbf == 2) { |
281 | | |
282 | | /* Current block either 1 by 1 or 2 by 2 */ |
283 | |
|
284 | 0 | nbnext = 1; |
285 | 0 | if (here + nbf + 1 <= *n) { |
286 | 0 | if (t[here + nbf + 1 + (here + nbf) * t_dim1] != 0.) { |
287 | 0 | nbnext = 2; |
288 | 0 | } |
289 | 0 | } |
290 | 0 | igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &here, & |
291 | 0 | nbf, &nbnext, &work[1], info); |
292 | 0 | if (*info != 0) { |
293 | 0 | *ilst = here; |
294 | 0 | return 0; |
295 | 0 | } |
296 | 0 | here += nbnext; |
297 | | |
298 | | /* Test if 2 by 2 block breaks into two 1 by 1 blocks */ |
299 | |
|
300 | 0 | if (nbf == 2) { |
301 | 0 | if (t[here + 1 + here * t_dim1] == 0.) { |
302 | 0 | nbf = 3; |
303 | 0 | } |
304 | 0 | } |
305 | |
|
306 | 0 | } else { |
307 | | |
308 | | /* Current block consists of two 1 by 1 blocks each of which |
309 | | must be swapped individually */ |
310 | |
|
311 | 0 | nbnext = 1; |
312 | 0 | if (here + 3 <= *n) { |
313 | 0 | if (t[here + 3 + (here + 2) * t_dim1] != 0.) { |
314 | 0 | nbnext = 2; |
315 | 0 | } |
316 | 0 | } |
317 | 0 | i__1 = here + 1; |
318 | 0 | igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &i__1, & |
319 | 0 | c__1, &nbnext, &work[1], info); |
320 | 0 | if (*info != 0) { |
321 | 0 | *ilst = here; |
322 | 0 | return 0; |
323 | 0 | } |
324 | 0 | if (nbnext == 1) { |
325 | | |
326 | | /* Swap two 1 by 1 blocks, no problems possible */ |
327 | |
|
328 | 0 | igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, & |
329 | 0 | here, &c__1, &nbnext, &work[1], info); |
330 | 0 | ++here; |
331 | 0 | } else { |
332 | | |
333 | | /* Recompute NBNEXT in case 2 by 2 split */ |
334 | |
|
335 | 0 | if (t[here + 2 + (here + 1) * t_dim1] == 0.) { |
336 | 0 | nbnext = 1; |
337 | 0 | } |
338 | 0 | if (nbnext == 2) { |
339 | | |
340 | | /* 2 by 2 Block did not split */ |
341 | |
|
342 | 0 | igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, & |
343 | 0 | here, &c__1, &nbnext, &work[1], info); |
344 | 0 | if (*info != 0) { |
345 | 0 | *ilst = here; |
346 | 0 | return 0; |
347 | 0 | } |
348 | 0 | here += 2; |
349 | 0 | } else { |
350 | | |
351 | | /* 2 by 2 Block did split */ |
352 | |
|
353 | 0 | igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, & |
354 | 0 | here, &c__1, &c__1, &work[1], info); |
355 | 0 | i__1 = here + 1; |
356 | 0 | igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, & |
357 | 0 | i__1, &c__1, &c__1, &work[1], info); |
358 | 0 | here += 2; |
359 | 0 | } |
360 | 0 | } |
361 | 0 | } |
362 | 0 | if (here < *ilst) { |
363 | 0 | goto L10; |
364 | 0 | } |
365 | |
|
366 | 0 | } else { |
367 | |
|
368 | 0 | here = *ifst; |
369 | 0 | L20: |
370 | | |
371 | | /* Swap block with next one above */ |
372 | |
|
373 | 0 | if (nbf == 1 || nbf == 2) { |
374 | | |
375 | | /* Current block either 1 by 1 or 2 by 2 */ |
376 | |
|
377 | 0 | nbnext = 1; |
378 | 0 | if (here >= 3) { |
379 | 0 | if (t[here - 1 + (here - 2) * t_dim1] != 0.) { |
380 | 0 | nbnext = 2; |
381 | 0 | } |
382 | 0 | } |
383 | 0 | i__1 = here - nbnext; |
384 | 0 | igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &i__1, & |
385 | 0 | nbnext, &nbf, &work[1], info); |
386 | 0 | if (*info != 0) { |
387 | 0 | *ilst = here; |
388 | 0 | return 0; |
389 | 0 | } |
390 | 0 | here -= nbnext; |
391 | | |
392 | | /* Test if 2 by 2 block breaks into two 1 by 1 blocks */ |
393 | |
|
394 | 0 | if (nbf == 2) { |
395 | 0 | if (t[here + 1 + here * t_dim1] == 0.) { |
396 | 0 | nbf = 3; |
397 | 0 | } |
398 | 0 | } |
399 | |
|
400 | 0 | } else { |
401 | | |
402 | | /* Current block consists of two 1 by 1 blocks each of which |
403 | | must be swapped individually */ |
404 | |
|
405 | 0 | nbnext = 1; |
406 | 0 | if (here >= 3) { |
407 | 0 | if (t[here - 1 + (here - 2) * t_dim1] != 0.) { |
408 | 0 | nbnext = 2; |
409 | 0 | } |
410 | 0 | } |
411 | 0 | i__1 = here - nbnext; |
412 | 0 | igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, &i__1, & |
413 | 0 | nbnext, &c__1, &work[1], info); |
414 | 0 | if (*info != 0) { |
415 | 0 | *ilst = here; |
416 | 0 | return 0; |
417 | 0 | } |
418 | 0 | if (nbnext == 1) { |
419 | | |
420 | | /* Swap two 1 by 1 blocks, no problems possible */ |
421 | |
|
422 | 0 | igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, & |
423 | 0 | here, &nbnext, &c__1, &work[1], info); |
424 | 0 | --here; |
425 | 0 | } else { |
426 | | |
427 | | /* Recompute NBNEXT in case 2 by 2 split */ |
428 | |
|
429 | 0 | if (t[here + (here - 1) * t_dim1] == 0.) { |
430 | 0 | nbnext = 1; |
431 | 0 | } |
432 | 0 | if (nbnext == 2) { |
433 | | |
434 | | /* 2 by 2 Block did not split */ |
435 | |
|
436 | 0 | i__1 = here - 1; |
437 | 0 | igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, & |
438 | 0 | i__1, &c__2, &c__1, &work[1], info); |
439 | 0 | if (*info != 0) { |
440 | 0 | *ilst = here; |
441 | 0 | return 0; |
442 | 0 | } |
443 | 0 | here += -2; |
444 | 0 | } else { |
445 | | |
446 | | /* 2 by 2 Block did split */ |
447 | |
|
448 | 0 | igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, & |
449 | 0 | here, &c__1, &c__1, &work[1], info); |
450 | 0 | i__1 = here - 1; |
451 | 0 | igraphdlaexc_(&wantq, n, &t[t_offset], ldt, &q[q_offset], ldq, & |
452 | 0 | i__1, &c__1, &c__1, &work[1], info); |
453 | 0 | here += -2; |
454 | 0 | } |
455 | 0 | } |
456 | 0 | } |
457 | 0 | if (here > *ilst) { |
458 | 0 | goto L20; |
459 | 0 | } |
460 | 0 | } |
461 | 0 | *ilst = here; |
462 | |
|
463 | 0 | return 0; |
464 | | |
465 | | /* End of DTREXC */ |
466 | |
|
467 | 0 | } /* igraphdtrexc_ */ |
468 | | |