1 /* ./src_f77/dsbgst.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 doublereal c_b8 = 0.;
11 static doublereal c_b9 = 1.;
12 static integer c__1 = 1;
13 static doublereal c_b20 = -1.;
14
dsbgst_(char * vect,char * uplo,integer * n,integer * ka,integer * kb,doublereal * ab,integer * ldab,doublereal * bb,integer * ldbb,doublereal * x,integer * ldx,doublereal * work,integer * info,ftnlen vect_len,ftnlen uplo_len)15 /* Subroutine */ int dsbgst_(char *vect, char *uplo, integer *n, integer *ka,
16 integer *kb, doublereal *ab, integer *ldab, doublereal *bb, integer *
17 ldbb, doublereal *x, integer *ldx, doublereal *work, integer *info,
18 ftnlen vect_len, ftnlen uplo_len)
19 {
20 /* System generated locals */
21 integer ab_dim1, ab_offset, bb_dim1, bb_offset, x_dim1, x_offset, i__1,
22 i__2, i__3, i__4;
23 doublereal d__1;
24
25 /* Local variables */
26 static integer i__, j, k, l, m;
27 static doublereal t;
28 static integer i0, i1, i2, j1, j2;
29 static doublereal ra;
30 static integer nr, nx, ka1, kb1;
31 static doublereal ra1;
32 static integer j1t, j2t;
33 static doublereal bii;
34 static integer kbt, nrt, inca;
35 extern /* Subroutine */ int dger_(integer *, integer *, doublereal *,
36 doublereal *, integer *, doublereal *, integer *, doublereal *,
37 integer *), drot_(integer *, doublereal *, integer *, doublereal *
38 , integer *, doublereal *, doublereal *), dscal_(integer *,
39 doublereal *, doublereal *, integer *);
40 extern logical lsame_(char *, char *, ftnlen, ftnlen);
41 static logical upper, wantx;
42 extern /* Subroutine */ int dlar2v_(integer *, doublereal *, doublereal *,
43 doublereal *, integer *, doublereal *, doublereal *, integer *),
44 dlaset_(char *, integer *, integer *, doublereal *, doublereal *,
45 doublereal *, integer *, ftnlen), dlartg_(doublereal *,
46 doublereal *, doublereal *, doublereal *, doublereal *), xerbla_(
47 char *, integer *, ftnlen), dlargv_(integer *, doublereal *,
48 integer *, doublereal *, integer *, doublereal *, integer *);
49 static logical update;
50 extern /* Subroutine */ int dlartv_(integer *, doublereal *, integer *,
51 doublereal *, integer *, doublereal *, doublereal *, integer *);
52
53
54 /* -- LAPACK routine (version 3.0) -- */
55 /* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
56 /* Courant Institute, Argonne National Lab, and Rice University */
57 /* June 30, 1999 */
58
59 /* .. Scalar Arguments .. */
60 /* .. */
61 /* .. Array Arguments .. */
62 /* .. */
63
64 /* Purpose */
65 /* ======= */
66
67 /* DSBGST reduces a real symmetric-definite banded generalized */
68 /* eigenproblem A*x = lambda*B*x to standard form C*y = lambda*y, */
69 /* such that C has the same bandwidth as A. */
70
71 /* B must have been previously factorized as S**T*S by DPBSTF, using a */
72 /* split Cholesky factorization. A is overwritten by C = X**T*A*X, where */
73 /* X = S**(-1)*Q and Q is an orthogonal matrix chosen to preserve the */
74 /* bandwidth of A. */
75
76 /* Arguments */
77 /* ========= */
78
79 /* VECT (input) CHARACTER*1 */
80 /* = 'N': do not form the transformation matrix X; */
81 /* = 'V': form X. */
82
83 /* UPLO (input) CHARACTER*1 */
84 /* = 'U': Upper triangle of A is stored; */
85 /* = 'L': Lower triangle of A is stored. */
86
87 /* N (input) INTEGER */
88 /* The order of the matrices A and B. N >= 0. */
89
90 /* KA (input) INTEGER */
91 /* The number of superdiagonals of the matrix A if UPLO = 'U', */
92 /* or the number of subdiagonals if UPLO = 'L'. KA >= 0. */
93
94 /* KB (input) INTEGER */
95 /* The number of superdiagonals of the matrix B if UPLO = 'U', */
96 /* or the number of subdiagonals if UPLO = 'L'. KA >= KB >= 0. */
97
98 /* AB (input/output) DOUBLE PRECISION array, dimension (LDAB,N) */
99 /* On entry, the upper or lower triangle of the symmetric band */
100 /* matrix A, stored in the first ka+1 rows of the array. The */
101 /* j-th column of A is stored in the j-th column of the array AB */
102 /* as follows: */
103 /* if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; */
104 /* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). */
105
106 /* On exit, the transformed matrix X**T*A*X, stored in the same */
107 /* format as A. */
108
109 /* LDAB (input) INTEGER */
110 /* The leading dimension of the array AB. LDAB >= KA+1. */
111
112 /* BB (input) DOUBLE PRECISION array, dimension (LDBB,N) */
113 /* The banded factor S from the split Cholesky factorization of */
114 /* B, as returned by DPBSTF, stored in the first KB+1 rows of */
115 /* the array. */
116
117 /* LDBB (input) INTEGER */
118 /* The leading dimension of the array BB. LDBB >= KB+1. */
119
120 /* X (output) DOUBLE PRECISION array, dimension (LDX,N) */
121 /* If VECT = 'V', the n-by-n matrix X. */
122 /* If VECT = 'N', the array X is not referenced. */
123
124 /* LDX (input) INTEGER */
125 /* The leading dimension of the array X. */
126 /* LDX >= max(1,N) if VECT = 'V'; LDX >= 1 otherwise. */
127
128 /* WORK (workspace) DOUBLE PRECISION array, dimension (2*N) */
129
130 /* INFO (output) INTEGER */
131 /* = 0: successful exit */
132 /* < 0: if INFO = -i, the i-th argument had an illegal value. */
133
134 /* ===================================================================== */
135
136 /* .. Parameters .. */
137 /* .. */
138 /* .. Local Scalars .. */
139 /* .. */
140 /* .. External Functions .. */
141 /* .. */
142 /* .. External Subroutines .. */
143 /* .. */
144 /* .. Intrinsic Functions .. */
145 /* .. */
146 /* .. Executable Statements .. */
147
148 /* Test the input parameters */
149
150 /* Parameter adjustments */
151 ab_dim1 = *ldab;
152 ab_offset = 1 + ab_dim1;
153 ab -= ab_offset;
154 bb_dim1 = *ldbb;
155 bb_offset = 1 + bb_dim1;
156 bb -= bb_offset;
157 x_dim1 = *ldx;
158 x_offset = 1 + x_dim1;
159 x -= x_offset;
160 --work;
161
162 /* Function Body */
163 wantx = lsame_(vect, "V", (ftnlen)1, (ftnlen)1);
164 upper = lsame_(uplo, "U", (ftnlen)1, (ftnlen)1);
165 ka1 = *ka + 1;
166 kb1 = *kb + 1;
167 *info = 0;
168 if (! wantx && ! lsame_(vect, "N", (ftnlen)1, (ftnlen)1)) {
169 *info = -1;
170 } else if (! upper && ! lsame_(uplo, "L", (ftnlen)1, (ftnlen)1)) {
171 *info = -2;
172 } else if (*n < 0) {
173 *info = -3;
174 } else if (*ka < 0) {
175 *info = -4;
176 } else if (*kb < 0) {
177 *info = -5;
178 } else if (*ldab < *ka + 1) {
179 *info = -7;
180 } else if (*ldbb < *kb + 1) {
181 *info = -9;
182 } else if (*ldx < 1 || wantx && *ldx < max(1,*n)) {
183 *info = -11;
184 }
185 if (*info != 0) {
186 i__1 = -(*info);
187 xerbla_("DSBGST", &i__1, (ftnlen)6);
188 return 0;
189 }
190
191 /* Quick return if possible */
192
193 if (*n == 0) {
194 return 0;
195 }
196
197 inca = *ldab * ka1;
198
199 /* Initialize X to the unit matrix, if needed */
200
201 if (wantx) {
202 dlaset_("Full", n, n, &c_b8, &c_b9, &x[x_offset], ldx, (ftnlen)4);
203 }
204
205 /* Set M to the splitting point m. It must be the same value as is */
206 /* used in DPBSTF. The chosen value allows the arrays WORK and RWORK */
207 /* to be of dimension (N). */
208
209 m = (*n + *kb) / 2;
210
211 /* The routine works in two phases, corresponding to the two halves */
212 /* of the split Cholesky factorization of B as S**T*S where */
213
214 /* S = ( U ) */
215 /* ( M L ) */
216
217 /* with U upper triangular of order m, and L lower triangular of */
218 /* order n-m. S has the same bandwidth as B. */
219
220 /* S is treated as a product of elementary matrices: */
221
222 /* S = S(m)*S(m-1)*...*S(2)*S(1)*S(m+1)*S(m+2)*...*S(n-1)*S(n) */
223
224 /* where S(i) is determined by the i-th row of S. */
225
226 /* In phase 1, the index i takes the values n, n-1, ... , m+1; */
227 /* in phase 2, it takes the values 1, 2, ... , m. */
228
229 /* For each value of i, the current matrix A is updated by forming */
230 /* inv(S(i))**T*A*inv(S(i)). This creates a triangular bulge outside */
231 /* the band of A. The bulge is then pushed down toward the bottom of */
232 /* A in phase 1, and up toward the top of A in phase 2, by applying */
233 /* plane rotations. */
234
235 /* There are kb*(kb+1)/2 elements in the bulge, but at most 2*kb-1 */
236 /* of them are linearly independent, so annihilating a bulge requires */
237 /* only 2*kb-1 plane rotations. The rotations are divided into a 1st */
238 /* set of kb-1 rotations, and a 2nd set of kb rotations. */
239
240 /* Wherever possible, rotations are generated and applied in vector */
241 /* operations of length NR between the indices J1 and J2 (sometimes */
242 /* replaced by modified values NRT, J1T or J2T). */
243
244 /* The cosines and sines of the rotations are stored in the array */
245 /* WORK. The cosines of the 1st set of rotations are stored in */
246 /* elements n+2:n+m-kb-1 and the sines of the 1st set in elements */
247 /* 2:m-kb-1; the cosines of the 2nd set are stored in elements */
248 /* n+m-kb+1:2*n and the sines of the second set in elements m-kb+1:n. */
249
250 /* The bulges are not formed explicitly; nonzero elements outside the */
251 /* band are created only when they are required for generating new */
252 /* rotations; they are stored in the array WORK, in positions where */
253 /* they are later overwritten by the sines of the rotations which */
254 /* annihilate them. */
255
256 /* **************************** Phase 1 ***************************** */
257
258 /* The logical structure of this phase is: */
259
260 /* UPDATE = .TRUE. */
261 /* DO I = N, M + 1, -1 */
262 /* use S(i) to update A and create a new bulge */
263 /* apply rotations to push all bulges KA positions downward */
264 /* END DO */
265 /* UPDATE = .FALSE. */
266 /* DO I = M + KA + 1, N - 1 */
267 /* apply rotations to push all bulges KA positions downward */
268 /* END DO */
269
270 /* To avoid duplicating code, the two loops are merged. */
271
272 update = TRUE_;
273 i__ = *n + 1;
274 L10:
275 if (update) {
276 --i__;
277 /* Computing MIN */
278 i__1 = *kb, i__2 = i__ - 1;
279 kbt = min(i__1,i__2);
280 i0 = i__ - 1;
281 /* Computing MIN */
282 i__1 = *n, i__2 = i__ + *ka;
283 i1 = min(i__1,i__2);
284 i2 = i__ - kbt + ka1;
285 if (i__ < m + 1) {
286 update = FALSE_;
287 ++i__;
288 i0 = m;
289 if (*ka == 0) {
290 goto L480;
291 }
292 goto L10;
293 }
294 } else {
295 i__ += *ka;
296 if (i__ > *n - 1) {
297 goto L480;
298 }
299 }
300
301 if (upper) {
302
303 /* Transform A, working with the upper triangle */
304
305 if (update) {
306
307 /* Form inv(S(i))**T * A * inv(S(i)) */
308
309 bii = bb[kb1 + i__ * bb_dim1];
310 i__1 = i1;
311 for (j = i__; j <= i__1; ++j) {
312 ab[i__ - j + ka1 + j * ab_dim1] /= bii;
313 /* L20: */
314 }
315 /* Computing MAX */
316 i__1 = 1, i__2 = i__ - *ka;
317 i__3 = i__;
318 for (j = max(i__1,i__2); j <= i__3; ++j) {
319 ab[j - i__ + ka1 + i__ * ab_dim1] /= bii;
320 /* L30: */
321 }
322 i__3 = i__ - 1;
323 for (k = i__ - kbt; k <= i__3; ++k) {
324 i__1 = k;
325 for (j = i__ - kbt; j <= i__1; ++j) {
326 ab[j - k + ka1 + k * ab_dim1] = ab[j - k + ka1 + k *
327 ab_dim1] - bb[j - i__ + kb1 + i__ * bb_dim1] * ab[
328 k - i__ + ka1 + i__ * ab_dim1] - bb[k - i__ + kb1
329 + i__ * bb_dim1] * ab[j - i__ + ka1 + i__ *
330 ab_dim1] + ab[ka1 + i__ * ab_dim1] * bb[j - i__ +
331 kb1 + i__ * bb_dim1] * bb[k - i__ + kb1 + i__ *
332 bb_dim1];
333 /* L40: */
334 }
335 /* Computing MAX */
336 i__1 = 1, i__2 = i__ - *ka;
337 i__4 = i__ - kbt - 1;
338 for (j = max(i__1,i__2); j <= i__4; ++j) {
339 ab[j - k + ka1 + k * ab_dim1] -= bb[k - i__ + kb1 + i__ *
340 bb_dim1] * ab[j - i__ + ka1 + i__ * ab_dim1];
341 /* L50: */
342 }
343 /* L60: */
344 }
345 i__3 = i1;
346 for (j = i__; j <= i__3; ++j) {
347 /* Computing MAX */
348 i__4 = j - *ka, i__1 = i__ - kbt;
349 i__2 = i__ - 1;
350 for (k = max(i__4,i__1); k <= i__2; ++k) {
351 ab[k - j + ka1 + j * ab_dim1] -= bb[k - i__ + kb1 + i__ *
352 bb_dim1] * ab[i__ - j + ka1 + j * ab_dim1];
353 /* L70: */
354 }
355 /* L80: */
356 }
357
358 if (wantx) {
359
360 /* post-multiply X by inv(S(i)) */
361
362 i__3 = *n - m;
363 d__1 = 1. / bii;
364 dscal_(&i__3, &d__1, &x[m + 1 + i__ * x_dim1], &c__1);
365 if (kbt > 0) {
366 i__3 = *n - m;
367 dger_(&i__3, &kbt, &c_b20, &x[m + 1 + i__ * x_dim1], &
368 c__1, &bb[kb1 - kbt + i__ * bb_dim1], &c__1, &x[m
369 + 1 + (i__ - kbt) * x_dim1], ldx);
370 }
371 }
372
373 /* store a(i,i1) in RA1 for use in next loop over K */
374
375 ra1 = ab[i__ - i1 + ka1 + i1 * ab_dim1];
376 }
377
378 /* Generate and apply vectors of rotations to chase all the */
379 /* existing bulges KA positions down toward the bottom of the */
380 /* band */
381
382 i__3 = *kb - 1;
383 for (k = 1; k <= i__3; ++k) {
384 if (update) {
385
386 /* Determine the rotations which would annihilate the bulge */
387 /* which has in theory just been created */
388
389 if (i__ - k + *ka < *n && i__ - k > 1) {
390
391 /* generate rotation to annihilate a(i,i-k+ka+1) */
392
393 dlartg_(&ab[k + 1 + (i__ - k + *ka) * ab_dim1], &ra1, &
394 work[*n + i__ - k + *ka - m], &work[i__ - k + *ka
395 - m], &ra);
396
397 /* create nonzero element a(i-k,i-k+ka+1) outside the */
398 /* band and store it in WORK(i-k) */
399
400 t = -bb[kb1 - k + i__ * bb_dim1] * ra1;
401 work[i__ - k] = work[*n + i__ - k + *ka - m] * t - work[
402 i__ - k + *ka - m] * ab[(i__ - k + *ka) * ab_dim1
403 + 1];
404 ab[(i__ - k + *ka) * ab_dim1 + 1] = work[i__ - k + *ka -
405 m] * t + work[*n + i__ - k + *ka - m] * ab[(i__ -
406 k + *ka) * ab_dim1 + 1];
407 ra1 = ra;
408 }
409 }
410 /* Computing MAX */
411 i__2 = 1, i__4 = k - i0 + 2;
412 j2 = i__ - k - 1 + max(i__2,i__4) * ka1;
413 nr = (*n - j2 + *ka) / ka1;
414 j1 = j2 + (nr - 1) * ka1;
415 if (update) {
416 /* Computing MAX */
417 i__2 = j2, i__4 = i__ + (*ka << 1) - k + 1;
418 j2t = max(i__2,i__4);
419 } else {
420 j2t = j2;
421 }
422 nrt = (*n - j2t + *ka) / ka1;
423 i__2 = j1;
424 i__4 = ka1;
425 for (j = j2t; i__4 < 0 ? j >= i__2 : j <= i__2; j += i__4) {
426
427 /* create nonzero element a(j-ka,j+1) outside the band */
428 /* and store it in WORK(j-m) */
429
430 work[j - m] *= ab[(j + 1) * ab_dim1 + 1];
431 ab[(j + 1) * ab_dim1 + 1] = work[*n + j - m] * ab[(j + 1) *
432 ab_dim1 + 1];
433 /* L90: */
434 }
435
436 /* generate rotations in 1st set to annihilate elements which */
437 /* have been created outside the band */
438
439 if (nrt > 0) {
440 dlargv_(&nrt, &ab[j2t * ab_dim1 + 1], &inca, &work[j2t - m], &
441 ka1, &work[*n + j2t - m], &ka1);
442 }
443 if (nr > 0) {
444
445 /* apply rotations in 1st set from the right */
446
447 i__4 = *ka - 1;
448 for (l = 1; l <= i__4; ++l) {
449 dlartv_(&nr, &ab[ka1 - l + j2 * ab_dim1], &inca, &ab[*ka
450 - l + (j2 + 1) * ab_dim1], &inca, &work[*n + j2 -
451 m], &work[j2 - m], &ka1);
452 /* L100: */
453 }
454
455 /* apply rotations in 1st set from both sides to diagonal */
456 /* blocks */
457
458 dlar2v_(&nr, &ab[ka1 + j2 * ab_dim1], &ab[ka1 + (j2 + 1) *
459 ab_dim1], &ab[*ka + (j2 + 1) * ab_dim1], &inca, &work[
460 *n + j2 - m], &work[j2 - m], &ka1);
461
462 }
463
464 /* start applying rotations in 1st set from the left */
465
466 i__4 = *kb - k + 1;
467 for (l = *ka - 1; l >= i__4; --l) {
468 nrt = (*n - j2 + l) / ka1;
469 if (nrt > 0) {
470 dlartv_(&nrt, &ab[l + (j2 + ka1 - l) * ab_dim1], &inca, &
471 ab[l + 1 + (j2 + ka1 - l) * ab_dim1], &inca, &
472 work[*n + j2 - m], &work[j2 - m], &ka1);
473 }
474 /* L110: */
475 }
476
477 if (wantx) {
478
479 /* post-multiply X by product of rotations in 1st set */
480
481 i__4 = j1;
482 i__2 = ka1;
483 for (j = j2; i__2 < 0 ? j >= i__4 : j <= i__4; j += i__2) {
484 i__1 = *n - m;
485 drot_(&i__1, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j
486 + 1) * x_dim1], &c__1, &work[*n + j - m], &work[j
487 - m]);
488 /* L120: */
489 }
490 }
491 /* L130: */
492 }
493
494 if (update) {
495 if (i2 <= *n && kbt > 0) {
496
497 /* create nonzero element a(i-kbt,i-kbt+ka+1) outside the */
498 /* band and store it in WORK(i-kbt) */
499
500 work[i__ - kbt] = -bb[kb1 - kbt + i__ * bb_dim1] * ra1;
501 }
502 }
503
504 for (k = *kb; k >= 1; --k) {
505 if (update) {
506 /* Computing MAX */
507 i__3 = 2, i__2 = k - i0 + 1;
508 j2 = i__ - k - 1 + max(i__3,i__2) * ka1;
509 } else {
510 /* Computing MAX */
511 i__3 = 1, i__2 = k - i0 + 1;
512 j2 = i__ - k - 1 + max(i__3,i__2) * ka1;
513 }
514
515 /* finish applying rotations in 2nd set from the left */
516
517 for (l = *kb - k; l >= 1; --l) {
518 nrt = (*n - j2 + *ka + l) / ka1;
519 if (nrt > 0) {
520 dlartv_(&nrt, &ab[l + (j2 - l + 1) * ab_dim1], &inca, &ab[
521 l + 1 + (j2 - l + 1) * ab_dim1], &inca, &work[*n
522 + j2 - *ka], &work[j2 - *ka], &ka1);
523 }
524 /* L140: */
525 }
526 nr = (*n - j2 + *ka) / ka1;
527 j1 = j2 + (nr - 1) * ka1;
528 i__3 = j2;
529 i__2 = -ka1;
530 for (j = j1; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) {
531 work[j] = work[j - *ka];
532 work[*n + j] = work[*n + j - *ka];
533 /* L150: */
534 }
535 i__2 = j1;
536 i__3 = ka1;
537 for (j = j2; i__3 < 0 ? j >= i__2 : j <= i__2; j += i__3) {
538
539 /* create nonzero element a(j-ka,j+1) outside the band */
540 /* and store it in WORK(j) */
541
542 work[j] *= ab[(j + 1) * ab_dim1 + 1];
543 ab[(j + 1) * ab_dim1 + 1] = work[*n + j] * ab[(j + 1) *
544 ab_dim1 + 1];
545 /* L160: */
546 }
547 if (update) {
548 if (i__ - k < *n - *ka && k <= kbt) {
549 work[i__ - k + *ka] = work[i__ - k];
550 }
551 }
552 /* L170: */
553 }
554
555 for (k = *kb; k >= 1; --k) {
556 /* Computing MAX */
557 i__3 = 1, i__2 = k - i0 + 1;
558 j2 = i__ - k - 1 + max(i__3,i__2) * ka1;
559 nr = (*n - j2 + *ka) / ka1;
560 j1 = j2 + (nr - 1) * ka1;
561 if (nr > 0) {
562
563 /* generate rotations in 2nd set to annihilate elements */
564 /* which have been created outside the band */
565
566 dlargv_(&nr, &ab[j2 * ab_dim1 + 1], &inca, &work[j2], &ka1, &
567 work[*n + j2], &ka1);
568
569 /* apply rotations in 2nd set from the right */
570
571 i__3 = *ka - 1;
572 for (l = 1; l <= i__3; ++l) {
573 dlartv_(&nr, &ab[ka1 - l + j2 * ab_dim1], &inca, &ab[*ka
574 - l + (j2 + 1) * ab_dim1], &inca, &work[*n + j2],
575 &work[j2], &ka1);
576 /* L180: */
577 }
578
579 /* apply rotations in 2nd set from both sides to diagonal */
580 /* blocks */
581
582 dlar2v_(&nr, &ab[ka1 + j2 * ab_dim1], &ab[ka1 + (j2 + 1) *
583 ab_dim1], &ab[*ka + (j2 + 1) * ab_dim1], &inca, &work[
584 *n + j2], &work[j2], &ka1);
585
586 }
587
588 /* start applying rotations in 2nd set from the left */
589
590 i__3 = *kb - k + 1;
591 for (l = *ka - 1; l >= i__3; --l) {
592 nrt = (*n - j2 + l) / ka1;
593 if (nrt > 0) {
594 dlartv_(&nrt, &ab[l + (j2 + ka1 - l) * ab_dim1], &inca, &
595 ab[l + 1 + (j2 + ka1 - l) * ab_dim1], &inca, &
596 work[*n + j2], &work[j2], &ka1);
597 }
598 /* L190: */
599 }
600
601 if (wantx) {
602
603 /* post-multiply X by product of rotations in 2nd set */
604
605 i__3 = j1;
606 i__2 = ka1;
607 for (j = j2; i__2 < 0 ? j >= i__3 : j <= i__3; j += i__2) {
608 i__4 = *n - m;
609 drot_(&i__4, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j
610 + 1) * x_dim1], &c__1, &work[*n + j], &work[j]);
611 /* L200: */
612 }
613 }
614 /* L210: */
615 }
616
617 i__2 = *kb - 1;
618 for (k = 1; k <= i__2; ++k) {
619 /* Computing MAX */
620 i__3 = 1, i__4 = k - i0 + 2;
621 j2 = i__ - k - 1 + max(i__3,i__4) * ka1;
622
623 /* finish applying rotations in 1st set from the left */
624
625 for (l = *kb - k; l >= 1; --l) {
626 nrt = (*n - j2 + l) / ka1;
627 if (nrt > 0) {
628 dlartv_(&nrt, &ab[l + (j2 + ka1 - l) * ab_dim1], &inca, &
629 ab[l + 1 + (j2 + ka1 - l) * ab_dim1], &inca, &
630 work[*n + j2 - m], &work[j2 - m], &ka1);
631 }
632 /* L220: */
633 }
634 /* L230: */
635 }
636
637 if (*kb > 1) {
638 i__2 = i__ - *kb + (*ka << 1) + 1;
639 for (j = *n - 1; j >= i__2; --j) {
640 work[*n + j - m] = work[*n + j - *ka - m];
641 work[j - m] = work[j - *ka - m];
642 /* L240: */
643 }
644 }
645
646 } else {
647
648 /* Transform A, working with the lower triangle */
649
650 if (update) {
651
652 /* Form inv(S(i))**T * A * inv(S(i)) */
653
654 bii = bb[i__ * bb_dim1 + 1];
655 i__2 = i1;
656 for (j = i__; j <= i__2; ++j) {
657 ab[j - i__ + 1 + i__ * ab_dim1] /= bii;
658 /* L250: */
659 }
660 /* Computing MAX */
661 i__2 = 1, i__3 = i__ - *ka;
662 i__4 = i__;
663 for (j = max(i__2,i__3); j <= i__4; ++j) {
664 ab[i__ - j + 1 + j * ab_dim1] /= bii;
665 /* L260: */
666 }
667 i__4 = i__ - 1;
668 for (k = i__ - kbt; k <= i__4; ++k) {
669 i__2 = k;
670 for (j = i__ - kbt; j <= i__2; ++j) {
671 ab[k - j + 1 + j * ab_dim1] = ab[k - j + 1 + j * ab_dim1]
672 - bb[i__ - j + 1 + j * bb_dim1] * ab[i__ - k + 1
673 + k * ab_dim1] - bb[i__ - k + 1 + k * bb_dim1] *
674 ab[i__ - j + 1 + j * ab_dim1] + ab[i__ * ab_dim1
675 + 1] * bb[i__ - j + 1 + j * bb_dim1] * bb[i__ - k
676 + 1 + k * bb_dim1];
677 /* L270: */
678 }
679 /* Computing MAX */
680 i__2 = 1, i__3 = i__ - *ka;
681 i__1 = i__ - kbt - 1;
682 for (j = max(i__2,i__3); j <= i__1; ++j) {
683 ab[k - j + 1 + j * ab_dim1] -= bb[i__ - k + 1 + k *
684 bb_dim1] * ab[i__ - j + 1 + j * ab_dim1];
685 /* L280: */
686 }
687 /* L290: */
688 }
689 i__4 = i1;
690 for (j = i__; j <= i__4; ++j) {
691 /* Computing MAX */
692 i__1 = j - *ka, i__2 = i__ - kbt;
693 i__3 = i__ - 1;
694 for (k = max(i__1,i__2); k <= i__3; ++k) {
695 ab[j - k + 1 + k * ab_dim1] -= bb[i__ - k + 1 + k *
696 bb_dim1] * ab[j - i__ + 1 + i__ * ab_dim1];
697 /* L300: */
698 }
699 /* L310: */
700 }
701
702 if (wantx) {
703
704 /* post-multiply X by inv(S(i)) */
705
706 i__4 = *n - m;
707 d__1 = 1. / bii;
708 dscal_(&i__4, &d__1, &x[m + 1 + i__ * x_dim1], &c__1);
709 if (kbt > 0) {
710 i__4 = *n - m;
711 i__3 = *ldbb - 1;
712 dger_(&i__4, &kbt, &c_b20, &x[m + 1 + i__ * x_dim1], &
713 c__1, &bb[kbt + 1 + (i__ - kbt) * bb_dim1], &i__3,
714 &x[m + 1 + (i__ - kbt) * x_dim1], ldx);
715 }
716 }
717
718 /* store a(i1,i) in RA1 for use in next loop over K */
719
720 ra1 = ab[i1 - i__ + 1 + i__ * ab_dim1];
721 }
722
723 /* Generate and apply vectors of rotations to chase all the */
724 /* existing bulges KA positions down toward the bottom of the */
725 /* band */
726
727 i__4 = *kb - 1;
728 for (k = 1; k <= i__4; ++k) {
729 if (update) {
730
731 /* Determine the rotations which would annihilate the bulge */
732 /* which has in theory just been created */
733
734 if (i__ - k + *ka < *n && i__ - k > 1) {
735
736 /* generate rotation to annihilate a(i-k+ka+1,i) */
737
738 dlartg_(&ab[ka1 - k + i__ * ab_dim1], &ra1, &work[*n +
739 i__ - k + *ka - m], &work[i__ - k + *ka - m], &ra)
740 ;
741
742 /* create nonzero element a(i-k+ka+1,i-k) outside the */
743 /* band and store it in WORK(i-k) */
744
745 t = -bb[k + 1 + (i__ - k) * bb_dim1] * ra1;
746 work[i__ - k] = work[*n + i__ - k + *ka - m] * t - work[
747 i__ - k + *ka - m] * ab[ka1 + (i__ - k) * ab_dim1]
748 ;
749 ab[ka1 + (i__ - k) * ab_dim1] = work[i__ - k + *ka - m] *
750 t + work[*n + i__ - k + *ka - m] * ab[ka1 + (i__
751 - k) * ab_dim1];
752 ra1 = ra;
753 }
754 }
755 /* Computing MAX */
756 i__3 = 1, i__1 = k - i0 + 2;
757 j2 = i__ - k - 1 + max(i__3,i__1) * ka1;
758 nr = (*n - j2 + *ka) / ka1;
759 j1 = j2 + (nr - 1) * ka1;
760 if (update) {
761 /* Computing MAX */
762 i__3 = j2, i__1 = i__ + (*ka << 1) - k + 1;
763 j2t = max(i__3,i__1);
764 } else {
765 j2t = j2;
766 }
767 nrt = (*n - j2t + *ka) / ka1;
768 i__3 = j1;
769 i__1 = ka1;
770 for (j = j2t; i__1 < 0 ? j >= i__3 : j <= i__3; j += i__1) {
771
772 /* create nonzero element a(j+1,j-ka) outside the band */
773 /* and store it in WORK(j-m) */
774
775 work[j - m] *= ab[ka1 + (j - *ka + 1) * ab_dim1];
776 ab[ka1 + (j - *ka + 1) * ab_dim1] = work[*n + j - m] * ab[ka1
777 + (j - *ka + 1) * ab_dim1];
778 /* L320: */
779 }
780
781 /* generate rotations in 1st set to annihilate elements which */
782 /* have been created outside the band */
783
784 if (nrt > 0) {
785 dlargv_(&nrt, &ab[ka1 + (j2t - *ka) * ab_dim1], &inca, &work[
786 j2t - m], &ka1, &work[*n + j2t - m], &ka1);
787 }
788 if (nr > 0) {
789
790 /* apply rotations in 1st set from the left */
791
792 i__1 = *ka - 1;
793 for (l = 1; l <= i__1; ++l) {
794 dlartv_(&nr, &ab[l + 1 + (j2 - l) * ab_dim1], &inca, &ab[
795 l + 2 + (j2 - l) * ab_dim1], &inca, &work[*n + j2
796 - m], &work[j2 - m], &ka1);
797 /* L330: */
798 }
799
800 /* apply rotations in 1st set from both sides to diagonal */
801 /* blocks */
802
803 dlar2v_(&nr, &ab[j2 * ab_dim1 + 1], &ab[(j2 + 1) * ab_dim1 +
804 1], &ab[j2 * ab_dim1 + 2], &inca, &work[*n + j2 - m],
805 &work[j2 - m], &ka1);
806
807 }
808
809 /* start applying rotations in 1st set from the right */
810
811 i__1 = *kb - k + 1;
812 for (l = *ka - 1; l >= i__1; --l) {
813 nrt = (*n - j2 + l) / ka1;
814 if (nrt > 0) {
815 dlartv_(&nrt, &ab[ka1 - l + 1 + j2 * ab_dim1], &inca, &ab[
816 ka1 - l + (j2 + 1) * ab_dim1], &inca, &work[*n +
817 j2 - m], &work[j2 - m], &ka1);
818 }
819 /* L340: */
820 }
821
822 if (wantx) {
823
824 /* post-multiply X by product of rotations in 1st set */
825
826 i__1 = j1;
827 i__3 = ka1;
828 for (j = j2; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) {
829 i__2 = *n - m;
830 drot_(&i__2, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j
831 + 1) * x_dim1], &c__1, &work[*n + j - m], &work[j
832 - m]);
833 /* L350: */
834 }
835 }
836 /* L360: */
837 }
838
839 if (update) {
840 if (i2 <= *n && kbt > 0) {
841
842 /* create nonzero element a(i-kbt+ka+1,i-kbt) outside the */
843 /* band and store it in WORK(i-kbt) */
844
845 work[i__ - kbt] = -bb[kbt + 1 + (i__ - kbt) * bb_dim1] * ra1;
846 }
847 }
848
849 for (k = *kb; k >= 1; --k) {
850 if (update) {
851 /* Computing MAX */
852 i__4 = 2, i__3 = k - i0 + 1;
853 j2 = i__ - k - 1 + max(i__4,i__3) * ka1;
854 } else {
855 /* Computing MAX */
856 i__4 = 1, i__3 = k - i0 + 1;
857 j2 = i__ - k - 1 + max(i__4,i__3) * ka1;
858 }
859
860 /* finish applying rotations in 2nd set from the right */
861
862 for (l = *kb - k; l >= 1; --l) {
863 nrt = (*n - j2 + *ka + l) / ka1;
864 if (nrt > 0) {
865 dlartv_(&nrt, &ab[ka1 - l + 1 + (j2 - *ka) * ab_dim1], &
866 inca, &ab[ka1 - l + (j2 - *ka + 1) * ab_dim1], &
867 inca, &work[*n + j2 - *ka], &work[j2 - *ka], &ka1)
868 ;
869 }
870 /* L370: */
871 }
872 nr = (*n - j2 + *ka) / ka1;
873 j1 = j2 + (nr - 1) * ka1;
874 i__4 = j2;
875 i__3 = -ka1;
876 for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
877 work[j] = work[j - *ka];
878 work[*n + j] = work[*n + j - *ka];
879 /* L380: */
880 }
881 i__3 = j1;
882 i__4 = ka1;
883 for (j = j2; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
884
885 /* create nonzero element a(j+1,j-ka) outside the band */
886 /* and store it in WORK(j) */
887
888 work[j] *= ab[ka1 + (j - *ka + 1) * ab_dim1];
889 ab[ka1 + (j - *ka + 1) * ab_dim1] = work[*n + j] * ab[ka1 + (
890 j - *ka + 1) * ab_dim1];
891 /* L390: */
892 }
893 if (update) {
894 if (i__ - k < *n - *ka && k <= kbt) {
895 work[i__ - k + *ka] = work[i__ - k];
896 }
897 }
898 /* L400: */
899 }
900
901 for (k = *kb; k >= 1; --k) {
902 /* Computing MAX */
903 i__4 = 1, i__3 = k - i0 + 1;
904 j2 = i__ - k - 1 + max(i__4,i__3) * ka1;
905 nr = (*n - j2 + *ka) / ka1;
906 j1 = j2 + (nr - 1) * ka1;
907 if (nr > 0) {
908
909 /* generate rotations in 2nd set to annihilate elements */
910 /* which have been created outside the band */
911
912 dlargv_(&nr, &ab[ka1 + (j2 - *ka) * ab_dim1], &inca, &work[j2]
913 , &ka1, &work[*n + j2], &ka1);
914
915 /* apply rotations in 2nd set from the left */
916
917 i__4 = *ka - 1;
918 for (l = 1; l <= i__4; ++l) {
919 dlartv_(&nr, &ab[l + 1 + (j2 - l) * ab_dim1], &inca, &ab[
920 l + 2 + (j2 - l) * ab_dim1], &inca, &work[*n + j2]
921 , &work[j2], &ka1);
922 /* L410: */
923 }
924
925 /* apply rotations in 2nd set from both sides to diagonal */
926 /* blocks */
927
928 dlar2v_(&nr, &ab[j2 * ab_dim1 + 1], &ab[(j2 + 1) * ab_dim1 +
929 1], &ab[j2 * ab_dim1 + 2], &inca, &work[*n + j2], &
930 work[j2], &ka1);
931
932 }
933
934 /* start applying rotations in 2nd set from the right */
935
936 i__4 = *kb - k + 1;
937 for (l = *ka - 1; l >= i__4; --l) {
938 nrt = (*n - j2 + l) / ka1;
939 if (nrt > 0) {
940 dlartv_(&nrt, &ab[ka1 - l + 1 + j2 * ab_dim1], &inca, &ab[
941 ka1 - l + (j2 + 1) * ab_dim1], &inca, &work[*n +
942 j2], &work[j2], &ka1);
943 }
944 /* L420: */
945 }
946
947 if (wantx) {
948
949 /* post-multiply X by product of rotations in 2nd set */
950
951 i__4 = j1;
952 i__3 = ka1;
953 for (j = j2; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
954 i__1 = *n - m;
955 drot_(&i__1, &x[m + 1 + j * x_dim1], &c__1, &x[m + 1 + (j
956 + 1) * x_dim1], &c__1, &work[*n + j], &work[j]);
957 /* L430: */
958 }
959 }
960 /* L440: */
961 }
962
963 i__3 = *kb - 1;
964 for (k = 1; k <= i__3; ++k) {
965 /* Computing MAX */
966 i__4 = 1, i__1 = k - i0 + 2;
967 j2 = i__ - k - 1 + max(i__4,i__1) * ka1;
968
969 /* finish applying rotations in 1st set from the right */
970
971 for (l = *kb - k; l >= 1; --l) {
972 nrt = (*n - j2 + l) / ka1;
973 if (nrt > 0) {
974 dlartv_(&nrt, &ab[ka1 - l + 1 + j2 * ab_dim1], &inca, &ab[
975 ka1 - l + (j2 + 1) * ab_dim1], &inca, &work[*n +
976 j2 - m], &work[j2 - m], &ka1);
977 }
978 /* L450: */
979 }
980 /* L460: */
981 }
982
983 if (*kb > 1) {
984 i__3 = i__ - *kb + (*ka << 1) + 1;
985 for (j = *n - 1; j >= i__3; --j) {
986 work[*n + j - m] = work[*n + j - *ka - m];
987 work[j - m] = work[j - *ka - m];
988 /* L470: */
989 }
990 }
991
992 }
993
994 goto L10;
995
996 L480:
997
998 /* **************************** Phase 2 ***************************** */
999
1000 /* The logical structure of this phase is: */
1001
1002 /* UPDATE = .TRUE. */
1003 /* DO I = 1, M */
1004 /* use S(i) to update A and create a new bulge */
1005 /* apply rotations to push all bulges KA positions upward */
1006 /* END DO */
1007 /* UPDATE = .FALSE. */
1008 /* DO I = M - KA - 1, 2, -1 */
1009 /* apply rotations to push all bulges KA positions upward */
1010 /* END DO */
1011
1012 /* To avoid duplicating code, the two loops are merged. */
1013
1014 update = TRUE_;
1015 i__ = 0;
1016 L490:
1017 if (update) {
1018 ++i__;
1019 /* Computing MIN */
1020 i__3 = *kb, i__4 = m - i__;
1021 kbt = min(i__3,i__4);
1022 i0 = i__ + 1;
1023 /* Computing MAX */
1024 i__3 = 1, i__4 = i__ - *ka;
1025 i1 = max(i__3,i__4);
1026 i2 = i__ + kbt - ka1;
1027 if (i__ > m) {
1028 update = FALSE_;
1029 --i__;
1030 i0 = m + 1;
1031 if (*ka == 0) {
1032 return 0;
1033 }
1034 goto L490;
1035 }
1036 } else {
1037 i__ -= *ka;
1038 if (i__ < 2) {
1039 return 0;
1040 }
1041 }
1042
1043 if (i__ < m - kbt) {
1044 nx = m;
1045 } else {
1046 nx = *n;
1047 }
1048
1049 if (upper) {
1050
1051 /* Transform A, working with the upper triangle */
1052
1053 if (update) {
1054
1055 /* Form inv(S(i))**T * A * inv(S(i)) */
1056
1057 bii = bb[kb1 + i__ * bb_dim1];
1058 i__3 = i__;
1059 for (j = i1; j <= i__3; ++j) {
1060 ab[j - i__ + ka1 + i__ * ab_dim1] /= bii;
1061 /* L500: */
1062 }
1063 /* Computing MIN */
1064 i__4 = *n, i__1 = i__ + *ka;
1065 i__3 = min(i__4,i__1);
1066 for (j = i__; j <= i__3; ++j) {
1067 ab[i__ - j + ka1 + j * ab_dim1] /= bii;
1068 /* L510: */
1069 }
1070 i__3 = i__ + kbt;
1071 for (k = i__ + 1; k <= i__3; ++k) {
1072 i__4 = i__ + kbt;
1073 for (j = k; j <= i__4; ++j) {
1074 ab[k - j + ka1 + j * ab_dim1] = ab[k - j + ka1 + j *
1075 ab_dim1] - bb[i__ - j + kb1 + j * bb_dim1] * ab[
1076 i__ - k + ka1 + k * ab_dim1] - bb[i__ - k + kb1 +
1077 k * bb_dim1] * ab[i__ - j + ka1 + j * ab_dim1] +
1078 ab[ka1 + i__ * ab_dim1] * bb[i__ - j + kb1 + j *
1079 bb_dim1] * bb[i__ - k + kb1 + k * bb_dim1];
1080 /* L520: */
1081 }
1082 /* Computing MIN */
1083 i__1 = *n, i__2 = i__ + *ka;
1084 i__4 = min(i__1,i__2);
1085 for (j = i__ + kbt + 1; j <= i__4; ++j) {
1086 ab[k - j + ka1 + j * ab_dim1] -= bb[i__ - k + kb1 + k *
1087 bb_dim1] * ab[i__ - j + ka1 + j * ab_dim1];
1088 /* L530: */
1089 }
1090 /* L540: */
1091 }
1092 i__3 = i__;
1093 for (j = i1; j <= i__3; ++j) {
1094 /* Computing MIN */
1095 i__1 = j + *ka, i__2 = i__ + kbt;
1096 i__4 = min(i__1,i__2);
1097 for (k = i__ + 1; k <= i__4; ++k) {
1098 ab[j - k + ka1 + k * ab_dim1] -= bb[i__ - k + kb1 + k *
1099 bb_dim1] * ab[j - i__ + ka1 + i__ * ab_dim1];
1100 /* L550: */
1101 }
1102 /* L560: */
1103 }
1104
1105 if (wantx) {
1106
1107 /* post-multiply X by inv(S(i)) */
1108
1109 d__1 = 1. / bii;
1110 dscal_(&nx, &d__1, &x[i__ * x_dim1 + 1], &c__1);
1111 if (kbt > 0) {
1112 i__3 = *ldbb - 1;
1113 dger_(&nx, &kbt, &c_b20, &x[i__ * x_dim1 + 1], &c__1, &bb[
1114 *kb + (i__ + 1) * bb_dim1], &i__3, &x[(i__ + 1) *
1115 x_dim1 + 1], ldx);
1116 }
1117 }
1118
1119 /* store a(i1,i) in RA1 for use in next loop over K */
1120
1121 ra1 = ab[i1 - i__ + ka1 + i__ * ab_dim1];
1122 }
1123
1124 /* Generate and apply vectors of rotations to chase all the */
1125 /* existing bulges KA positions up toward the top of the band */
1126
1127 i__3 = *kb - 1;
1128 for (k = 1; k <= i__3; ++k) {
1129 if (update) {
1130
1131 /* Determine the rotations which would annihilate the bulge */
1132 /* which has in theory just been created */
1133
1134 if (i__ + k - ka1 > 0 && i__ + k < m) {
1135
1136 /* generate rotation to annihilate a(i+k-ka-1,i) */
1137
1138 dlartg_(&ab[k + 1 + i__ * ab_dim1], &ra1, &work[*n + i__
1139 + k - *ka], &work[i__ + k - *ka], &ra);
1140
1141 /* create nonzero element a(i+k-ka-1,i+k) outside the */
1142 /* band and store it in WORK(m-kb+i+k) */
1143
1144 t = -bb[kb1 - k + (i__ + k) * bb_dim1] * ra1;
1145 work[m - *kb + i__ + k] = work[*n + i__ + k - *ka] * t -
1146 work[i__ + k - *ka] * ab[(i__ + k) * ab_dim1 + 1];
1147 ab[(i__ + k) * ab_dim1 + 1] = work[i__ + k - *ka] * t +
1148 work[*n + i__ + k - *ka] * ab[(i__ + k) * ab_dim1
1149 + 1];
1150 ra1 = ra;
1151 }
1152 }
1153 /* Computing MAX */
1154 i__4 = 1, i__1 = k + i0 - m + 1;
1155 j2 = i__ + k + 1 - max(i__4,i__1) * ka1;
1156 nr = (j2 + *ka - 1) / ka1;
1157 j1 = j2 - (nr - 1) * ka1;
1158 if (update) {
1159 /* Computing MIN */
1160 i__4 = j2, i__1 = i__ - (*ka << 1) + k - 1;
1161 j2t = min(i__4,i__1);
1162 } else {
1163 j2t = j2;
1164 }
1165 nrt = (j2t + *ka - 1) / ka1;
1166 i__4 = j2t;
1167 i__1 = ka1;
1168 for (j = j1; i__1 < 0 ? j >= i__4 : j <= i__4; j += i__1) {
1169
1170 /* create nonzero element a(j-1,j+ka) outside the band */
1171 /* and store it in WORK(j) */
1172
1173 work[j] *= ab[(j + *ka - 1) * ab_dim1 + 1];
1174 ab[(j + *ka - 1) * ab_dim1 + 1] = work[*n + j] * ab[(j + *ka
1175 - 1) * ab_dim1 + 1];
1176 /* L570: */
1177 }
1178
1179 /* generate rotations in 1st set to annihilate elements which */
1180 /* have been created outside the band */
1181
1182 if (nrt > 0) {
1183 dlargv_(&nrt, &ab[(j1 + *ka) * ab_dim1 + 1], &inca, &work[j1],
1184 &ka1, &work[*n + j1], &ka1);
1185 }
1186 if (nr > 0) {
1187
1188 /* apply rotations in 1st set from the left */
1189
1190 i__1 = *ka - 1;
1191 for (l = 1; l <= i__1; ++l) {
1192 dlartv_(&nr, &ab[ka1 - l + (j1 + l) * ab_dim1], &inca, &
1193 ab[*ka - l + (j1 + l) * ab_dim1], &inca, &work[*n
1194 + j1], &work[j1], &ka1);
1195 /* L580: */
1196 }
1197
1198 /* apply rotations in 1st set from both sides to diagonal */
1199 /* blocks */
1200
1201 dlar2v_(&nr, &ab[ka1 + j1 * ab_dim1], &ab[ka1 + (j1 - 1) *
1202 ab_dim1], &ab[*ka + j1 * ab_dim1], &inca, &work[*n +
1203 j1], &work[j1], &ka1);
1204
1205 }
1206
1207 /* start applying rotations in 1st set from the right */
1208
1209 i__1 = *kb - k + 1;
1210 for (l = *ka - 1; l >= i__1; --l) {
1211 nrt = (j2 + l - 1) / ka1;
1212 j1t = j2 - (nrt - 1) * ka1;
1213 if (nrt > 0) {
1214 dlartv_(&nrt, &ab[l + j1t * ab_dim1], &inca, &ab[l + 1 + (
1215 j1t - 1) * ab_dim1], &inca, &work[*n + j1t], &
1216 work[j1t], &ka1);
1217 }
1218 /* L590: */
1219 }
1220
1221 if (wantx) {
1222
1223 /* post-multiply X by product of rotations in 1st set */
1224
1225 i__1 = j2;
1226 i__4 = ka1;
1227 for (j = j1; i__4 < 0 ? j >= i__1 : j <= i__1; j += i__4) {
1228 drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1
1229 + 1], &c__1, &work[*n + j], &work[j]);
1230 /* L600: */
1231 }
1232 }
1233 /* L610: */
1234 }
1235
1236 if (update) {
1237 if (i2 > 0 && kbt > 0) {
1238
1239 /* create nonzero element a(i+kbt-ka-1,i+kbt) outside the */
1240 /* band and store it in WORK(m-kb+i+kbt) */
1241
1242 work[m - *kb + i__ + kbt] = -bb[kb1 - kbt + (i__ + kbt) *
1243 bb_dim1] * ra1;
1244 }
1245 }
1246
1247 for (k = *kb; k >= 1; --k) {
1248 if (update) {
1249 /* Computing MAX */
1250 i__3 = 2, i__4 = k + i0 - m;
1251 j2 = i__ + k + 1 - max(i__3,i__4) * ka1;
1252 } else {
1253 /* Computing MAX */
1254 i__3 = 1, i__4 = k + i0 - m;
1255 j2 = i__ + k + 1 - max(i__3,i__4) * ka1;
1256 }
1257
1258 /* finish applying rotations in 2nd set from the right */
1259
1260 for (l = *kb - k; l >= 1; --l) {
1261 nrt = (j2 + *ka + l - 1) / ka1;
1262 j1t = j2 - (nrt - 1) * ka1;
1263 if (nrt > 0) {
1264 dlartv_(&nrt, &ab[l + (j1t + *ka) * ab_dim1], &inca, &ab[
1265 l + 1 + (j1t + *ka - 1) * ab_dim1], &inca, &work[*
1266 n + m - *kb + j1t + *ka], &work[m - *kb + j1t + *
1267 ka], &ka1);
1268 }
1269 /* L620: */
1270 }
1271 nr = (j2 + *ka - 1) / ka1;
1272 j1 = j2 - (nr - 1) * ka1;
1273 i__3 = j2;
1274 i__4 = ka1;
1275 for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
1276 work[m - *kb + j] = work[m - *kb + j + *ka];
1277 work[*n + m - *kb + j] = work[*n + m - *kb + j + *ka];
1278 /* L630: */
1279 }
1280 i__4 = j2;
1281 i__3 = ka1;
1282 for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
1283
1284 /* create nonzero element a(j-1,j+ka) outside the band */
1285 /* and store it in WORK(m-kb+j) */
1286
1287 work[m - *kb + j] *= ab[(j + *ka - 1) * ab_dim1 + 1];
1288 ab[(j + *ka - 1) * ab_dim1 + 1] = work[*n + m - *kb + j] * ab[
1289 (j + *ka - 1) * ab_dim1 + 1];
1290 /* L640: */
1291 }
1292 if (update) {
1293 if (i__ + k > ka1 && k <= kbt) {
1294 work[m - *kb + i__ + k - *ka] = work[m - *kb + i__ + k];
1295 }
1296 }
1297 /* L650: */
1298 }
1299
1300 for (k = *kb; k >= 1; --k) {
1301 /* Computing MAX */
1302 i__3 = 1, i__4 = k + i0 - m;
1303 j2 = i__ + k + 1 - max(i__3,i__4) * ka1;
1304 nr = (j2 + *ka - 1) / ka1;
1305 j1 = j2 - (nr - 1) * ka1;
1306 if (nr > 0) {
1307
1308 /* generate rotations in 2nd set to annihilate elements */
1309 /* which have been created outside the band */
1310
1311 dlargv_(&nr, &ab[(j1 + *ka) * ab_dim1 + 1], &inca, &work[m - *
1312 kb + j1], &ka1, &work[*n + m - *kb + j1], &ka1);
1313
1314 /* apply rotations in 2nd set from the left */
1315
1316 i__3 = *ka - 1;
1317 for (l = 1; l <= i__3; ++l) {
1318 dlartv_(&nr, &ab[ka1 - l + (j1 + l) * ab_dim1], &inca, &
1319 ab[*ka - l + (j1 + l) * ab_dim1], &inca, &work[*n
1320 + m - *kb + j1], &work[m - *kb + j1], &ka1);
1321 /* L660: */
1322 }
1323
1324 /* apply rotations in 2nd set from both sides to diagonal */
1325 /* blocks */
1326
1327 dlar2v_(&nr, &ab[ka1 + j1 * ab_dim1], &ab[ka1 + (j1 - 1) *
1328 ab_dim1], &ab[*ka + j1 * ab_dim1], &inca, &work[*n +
1329 m - *kb + j1], &work[m - *kb + j1], &ka1);
1330
1331 }
1332
1333 /* start applying rotations in 2nd set from the right */
1334
1335 i__3 = *kb - k + 1;
1336 for (l = *ka - 1; l >= i__3; --l) {
1337 nrt = (j2 + l - 1) / ka1;
1338 j1t = j2 - (nrt - 1) * ka1;
1339 if (nrt > 0) {
1340 dlartv_(&nrt, &ab[l + j1t * ab_dim1], &inca, &ab[l + 1 + (
1341 j1t - 1) * ab_dim1], &inca, &work[*n + m - *kb +
1342 j1t], &work[m - *kb + j1t], &ka1);
1343 }
1344 /* L670: */
1345 }
1346
1347 if (wantx) {
1348
1349 /* post-multiply X by product of rotations in 2nd set */
1350
1351 i__3 = j2;
1352 i__4 = ka1;
1353 for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
1354 drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1
1355 + 1], &c__1, &work[*n + m - *kb + j], &work[m - *
1356 kb + j]);
1357 /* L680: */
1358 }
1359 }
1360 /* L690: */
1361 }
1362
1363 i__4 = *kb - 1;
1364 for (k = 1; k <= i__4; ++k) {
1365 /* Computing MAX */
1366 i__3 = 1, i__1 = k + i0 - m + 1;
1367 j2 = i__ + k + 1 - max(i__3,i__1) * ka1;
1368
1369 /* finish applying rotations in 1st set from the right */
1370
1371 for (l = *kb - k; l >= 1; --l) {
1372 nrt = (j2 + l - 1) / ka1;
1373 j1t = j2 - (nrt - 1) * ka1;
1374 if (nrt > 0) {
1375 dlartv_(&nrt, &ab[l + j1t * ab_dim1], &inca, &ab[l + 1 + (
1376 j1t - 1) * ab_dim1], &inca, &work[*n + j1t], &
1377 work[j1t], &ka1);
1378 }
1379 /* L700: */
1380 }
1381 /* L710: */
1382 }
1383
1384 if (*kb > 1) {
1385 /* Computing MIN */
1386 i__3 = i__ + *kb;
1387 i__4 = min(i__3,m) - (*ka << 1) - 1;
1388 for (j = 2; j <= i__4; ++j) {
1389 work[*n + j] = work[*n + j + *ka];
1390 work[j] = work[j + *ka];
1391 /* L720: */
1392 }
1393 }
1394
1395 } else {
1396
1397 /* Transform A, working with the lower triangle */
1398
1399 if (update) {
1400
1401 /* Form inv(S(i))**T * A * inv(S(i)) */
1402
1403 bii = bb[i__ * bb_dim1 + 1];
1404 i__4 = i__;
1405 for (j = i1; j <= i__4; ++j) {
1406 ab[i__ - j + 1 + j * ab_dim1] /= bii;
1407 /* L730: */
1408 }
1409 /* Computing MIN */
1410 i__3 = *n, i__1 = i__ + *ka;
1411 i__4 = min(i__3,i__1);
1412 for (j = i__; j <= i__4; ++j) {
1413 ab[j - i__ + 1 + i__ * ab_dim1] /= bii;
1414 /* L740: */
1415 }
1416 i__4 = i__ + kbt;
1417 for (k = i__ + 1; k <= i__4; ++k) {
1418 i__3 = i__ + kbt;
1419 for (j = k; j <= i__3; ++j) {
1420 ab[j - k + 1 + k * ab_dim1] = ab[j - k + 1 + k * ab_dim1]
1421 - bb[j - i__ + 1 + i__ * bb_dim1] * ab[k - i__ +
1422 1 + i__ * ab_dim1] - bb[k - i__ + 1 + i__ *
1423 bb_dim1] * ab[j - i__ + 1 + i__ * ab_dim1] + ab[
1424 i__ * ab_dim1 + 1] * bb[j - i__ + 1 + i__ *
1425 bb_dim1] * bb[k - i__ + 1 + i__ * bb_dim1];
1426 /* L750: */
1427 }
1428 /* Computing MIN */
1429 i__1 = *n, i__2 = i__ + *ka;
1430 i__3 = min(i__1,i__2);
1431 for (j = i__ + kbt + 1; j <= i__3; ++j) {
1432 ab[j - k + 1 + k * ab_dim1] -= bb[k - i__ + 1 + i__ *
1433 bb_dim1] * ab[j - i__ + 1 + i__ * ab_dim1];
1434 /* L760: */
1435 }
1436 /* L770: */
1437 }
1438 i__4 = i__;
1439 for (j = i1; j <= i__4; ++j) {
1440 /* Computing MIN */
1441 i__1 = j + *ka, i__2 = i__ + kbt;
1442 i__3 = min(i__1,i__2);
1443 for (k = i__ + 1; k <= i__3; ++k) {
1444 ab[k - j + 1 + j * ab_dim1] -= bb[k - i__ + 1 + i__ *
1445 bb_dim1] * ab[i__ - j + 1 + j * ab_dim1];
1446 /* L780: */
1447 }
1448 /* L790: */
1449 }
1450
1451 if (wantx) {
1452
1453 /* post-multiply X by inv(S(i)) */
1454
1455 d__1 = 1. / bii;
1456 dscal_(&nx, &d__1, &x[i__ * x_dim1 + 1], &c__1);
1457 if (kbt > 0) {
1458 dger_(&nx, &kbt, &c_b20, &x[i__ * x_dim1 + 1], &c__1, &bb[
1459 i__ * bb_dim1 + 2], &c__1, &x[(i__ + 1) * x_dim1
1460 + 1], ldx);
1461 }
1462 }
1463
1464 /* store a(i,i1) in RA1 for use in next loop over K */
1465
1466 ra1 = ab[i__ - i1 + 1 + i1 * ab_dim1];
1467 }
1468
1469 /* Generate and apply vectors of rotations to chase all the */
1470 /* existing bulges KA positions up toward the top of the band */
1471
1472 i__4 = *kb - 1;
1473 for (k = 1; k <= i__4; ++k) {
1474 if (update) {
1475
1476 /* Determine the rotations which would annihilate the bulge */
1477 /* which has in theory just been created */
1478
1479 if (i__ + k - ka1 > 0 && i__ + k < m) {
1480
1481 /* generate rotation to annihilate a(i,i+k-ka-1) */
1482
1483 dlartg_(&ab[ka1 - k + (i__ + k - *ka) * ab_dim1], &ra1, &
1484 work[*n + i__ + k - *ka], &work[i__ + k - *ka], &
1485 ra);
1486
1487 /* create nonzero element a(i+k,i+k-ka-1) outside the */
1488 /* band and store it in WORK(m-kb+i+k) */
1489
1490 t = -bb[k + 1 + i__ * bb_dim1] * ra1;
1491 work[m - *kb + i__ + k] = work[*n + i__ + k - *ka] * t -
1492 work[i__ + k - *ka] * ab[ka1 + (i__ + k - *ka) *
1493 ab_dim1];
1494 ab[ka1 + (i__ + k - *ka) * ab_dim1] = work[i__ + k - *ka]
1495 * t + work[*n + i__ + k - *ka] * ab[ka1 + (i__ +
1496 k - *ka) * ab_dim1];
1497 ra1 = ra;
1498 }
1499 }
1500 /* Computing MAX */
1501 i__3 = 1, i__1 = k + i0 - m + 1;
1502 j2 = i__ + k + 1 - max(i__3,i__1) * ka1;
1503 nr = (j2 + *ka - 1) / ka1;
1504 j1 = j2 - (nr - 1) * ka1;
1505 if (update) {
1506 /* Computing MIN */
1507 i__3 = j2, i__1 = i__ - (*ka << 1) + k - 1;
1508 j2t = min(i__3,i__1);
1509 } else {
1510 j2t = j2;
1511 }
1512 nrt = (j2t + *ka - 1) / ka1;
1513 i__3 = j2t;
1514 i__1 = ka1;
1515 for (j = j1; i__1 < 0 ? j >= i__3 : j <= i__3; j += i__1) {
1516
1517 /* create nonzero element a(j+ka,j-1) outside the band */
1518 /* and store it in WORK(j) */
1519
1520 work[j] *= ab[ka1 + (j - 1) * ab_dim1];
1521 ab[ka1 + (j - 1) * ab_dim1] = work[*n + j] * ab[ka1 + (j - 1)
1522 * ab_dim1];
1523 /* L800: */
1524 }
1525
1526 /* generate rotations in 1st set to annihilate elements which */
1527 /* have been created outside the band */
1528
1529 if (nrt > 0) {
1530 dlargv_(&nrt, &ab[ka1 + j1 * ab_dim1], &inca, &work[j1], &ka1,
1531 &work[*n + j1], &ka1);
1532 }
1533 if (nr > 0) {
1534
1535 /* apply rotations in 1st set from the right */
1536
1537 i__1 = *ka - 1;
1538 for (l = 1; l <= i__1; ++l) {
1539 dlartv_(&nr, &ab[l + 1 + j1 * ab_dim1], &inca, &ab[l + 2
1540 + (j1 - 1) * ab_dim1], &inca, &work[*n + j1], &
1541 work[j1], &ka1);
1542 /* L810: */
1543 }
1544
1545 /* apply rotations in 1st set from both sides to diagonal */
1546 /* blocks */
1547
1548 dlar2v_(&nr, &ab[j1 * ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 +
1549 1], &ab[(j1 - 1) * ab_dim1 + 2], &inca, &work[*n + j1]
1550 , &work[j1], &ka1);
1551
1552 }
1553
1554 /* start applying rotations in 1st set from the left */
1555
1556 i__1 = *kb - k + 1;
1557 for (l = *ka - 1; l >= i__1; --l) {
1558 nrt = (j2 + l - 1) / ka1;
1559 j1t = j2 - (nrt - 1) * ka1;
1560 if (nrt > 0) {
1561 dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t - ka1 + l) * ab_dim1]
1562 , &inca, &ab[ka1 - l + (j1t - ka1 + l) * ab_dim1],
1563 &inca, &work[*n + j1t], &work[j1t], &ka1);
1564 }
1565 /* L820: */
1566 }
1567
1568 if (wantx) {
1569
1570 /* post-multiply X by product of rotations in 1st set */
1571
1572 i__1 = j2;
1573 i__3 = ka1;
1574 for (j = j1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) {
1575 drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1
1576 + 1], &c__1, &work[*n + j], &work[j]);
1577 /* L830: */
1578 }
1579 }
1580 /* L840: */
1581 }
1582
1583 if (update) {
1584 if (i2 > 0 && kbt > 0) {
1585
1586 /* create nonzero element a(i+kbt,i+kbt-ka-1) outside the */
1587 /* band and store it in WORK(m-kb+i+kbt) */
1588
1589 work[m - *kb + i__ + kbt] = -bb[kbt + 1 + i__ * bb_dim1] *
1590 ra1;
1591 }
1592 }
1593
1594 for (k = *kb; k >= 1; --k) {
1595 if (update) {
1596 /* Computing MAX */
1597 i__4 = 2, i__3 = k + i0 - m;
1598 j2 = i__ + k + 1 - max(i__4,i__3) * ka1;
1599 } else {
1600 /* Computing MAX */
1601 i__4 = 1, i__3 = k + i0 - m;
1602 j2 = i__ + k + 1 - max(i__4,i__3) * ka1;
1603 }
1604
1605 /* finish applying rotations in 2nd set from the left */
1606
1607 for (l = *kb - k; l >= 1; --l) {
1608 nrt = (j2 + *ka + l - 1) / ka1;
1609 j1t = j2 - (nrt - 1) * ka1;
1610 if (nrt > 0) {
1611 dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t + l - 1) * ab_dim1],
1612 &inca, &ab[ka1 - l + (j1t + l - 1) * ab_dim1], &
1613 inca, &work[*n + m - *kb + j1t + *ka], &work[m - *
1614 kb + j1t + *ka], &ka1);
1615 }
1616 /* L850: */
1617 }
1618 nr = (j2 + *ka - 1) / ka1;
1619 j1 = j2 - (nr - 1) * ka1;
1620 i__4 = j2;
1621 i__3 = ka1;
1622 for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
1623 work[m - *kb + j] = work[m - *kb + j + *ka];
1624 work[*n + m - *kb + j] = work[*n + m - *kb + j + *ka];
1625 /* L860: */
1626 }
1627 i__3 = j2;
1628 i__4 = ka1;
1629 for (j = j1; i__4 < 0 ? j >= i__3 : j <= i__3; j += i__4) {
1630
1631 /* create nonzero element a(j+ka,j-1) outside the band */
1632 /* and store it in WORK(m-kb+j) */
1633
1634 work[m - *kb + j] *= ab[ka1 + (j - 1) * ab_dim1];
1635 ab[ka1 + (j - 1) * ab_dim1] = work[*n + m - *kb + j] * ab[ka1
1636 + (j - 1) * ab_dim1];
1637 /* L870: */
1638 }
1639 if (update) {
1640 if (i__ + k > ka1 && k <= kbt) {
1641 work[m - *kb + i__ + k - *ka] = work[m - *kb + i__ + k];
1642 }
1643 }
1644 /* L880: */
1645 }
1646
1647 for (k = *kb; k >= 1; --k) {
1648 /* Computing MAX */
1649 i__4 = 1, i__3 = k + i0 - m;
1650 j2 = i__ + k + 1 - max(i__4,i__3) * ka1;
1651 nr = (j2 + *ka - 1) / ka1;
1652 j1 = j2 - (nr - 1) * ka1;
1653 if (nr > 0) {
1654
1655 /* generate rotations in 2nd set to annihilate elements */
1656 /* which have been created outside the band */
1657
1658 dlargv_(&nr, &ab[ka1 + j1 * ab_dim1], &inca, &work[m - *kb +
1659 j1], &ka1, &work[*n + m - *kb + j1], &ka1);
1660
1661 /* apply rotations in 2nd set from the right */
1662
1663 i__4 = *ka - 1;
1664 for (l = 1; l <= i__4; ++l) {
1665 dlartv_(&nr, &ab[l + 1 + j1 * ab_dim1], &inca, &ab[l + 2
1666 + (j1 - 1) * ab_dim1], &inca, &work[*n + m - *kb
1667 + j1], &work[m - *kb + j1], &ka1);
1668 /* L890: */
1669 }
1670
1671 /* apply rotations in 2nd set from both sides to diagonal */
1672 /* blocks */
1673
1674 dlar2v_(&nr, &ab[j1 * ab_dim1 + 1], &ab[(j1 - 1) * ab_dim1 +
1675 1], &ab[(j1 - 1) * ab_dim1 + 2], &inca, &work[*n + m
1676 - *kb + j1], &work[m - *kb + j1], &ka1);
1677
1678 }
1679
1680 /* start applying rotations in 2nd set from the left */
1681
1682 i__4 = *kb - k + 1;
1683 for (l = *ka - 1; l >= i__4; --l) {
1684 nrt = (j2 + l - 1) / ka1;
1685 j1t = j2 - (nrt - 1) * ka1;
1686 if (nrt > 0) {
1687 dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t - ka1 + l) * ab_dim1]
1688 , &inca, &ab[ka1 - l + (j1t - ka1 + l) * ab_dim1],
1689 &inca, &work[*n + m - *kb + j1t], &work[m - *kb
1690 + j1t], &ka1);
1691 }
1692 /* L900: */
1693 }
1694
1695 if (wantx) {
1696
1697 /* post-multiply X by product of rotations in 2nd set */
1698
1699 i__4 = j2;
1700 i__3 = ka1;
1701 for (j = j1; i__3 < 0 ? j >= i__4 : j <= i__4; j += i__3) {
1702 drot_(&nx, &x[j * x_dim1 + 1], &c__1, &x[(j - 1) * x_dim1
1703 + 1], &c__1, &work[*n + m - *kb + j], &work[m - *
1704 kb + j]);
1705 /* L910: */
1706 }
1707 }
1708 /* L920: */
1709 }
1710
1711 i__3 = *kb - 1;
1712 for (k = 1; k <= i__3; ++k) {
1713 /* Computing MAX */
1714 i__4 = 1, i__1 = k + i0 - m + 1;
1715 j2 = i__ + k + 1 - max(i__4,i__1) * ka1;
1716
1717 /* finish applying rotations in 1st set from the left */
1718
1719 for (l = *kb - k; l >= 1; --l) {
1720 nrt = (j2 + l - 1) / ka1;
1721 j1t = j2 - (nrt - 1) * ka1;
1722 if (nrt > 0) {
1723 dlartv_(&nrt, &ab[ka1 - l + 1 + (j1t - ka1 + l) * ab_dim1]
1724 , &inca, &ab[ka1 - l + (j1t - ka1 + l) * ab_dim1],
1725 &inca, &work[*n + j1t], &work[j1t], &ka1);
1726 }
1727 /* L930: */
1728 }
1729 /* L940: */
1730 }
1731
1732 if (*kb > 1) {
1733 /* Computing MIN */
1734 i__4 = i__ + *kb;
1735 i__3 = min(i__4,m) - (*ka << 1) - 1;
1736 for (j = 2; j <= i__3; ++j) {
1737 work[*n + j] = work[*n + j + *ka];
1738 work[j] = work[j + *ka];
1739 /* L950: */
1740 }
1741 }
1742
1743 }
1744
1745 goto L490;
1746
1747 /* End of DSBGST */
1748
1749 } /* dsbgst_ */
1750
1751