LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ csytrf_aa_2stage()

 subroutine csytrf_aa_2stage ( character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, complex, dimension( * ) work, integer lwork, integer info )

CSYTRF_AA_2STAGE

Purpose:
``` CSYTRF_AA_2STAGE computes the factorization of a complex symmetric matrix A
using the Aasen's algorithm.  The form of the factorization is

A = U**T*T*U  or  A = L*T*L**T

where U (or L) is a product of permutation and unit upper (lower)
triangular matrices, and T is a complex symmetric band matrix with the
bandwidth of NB (NB is internally selected and stored in TB( 1 ), and T is
LU factorized with partial pivoting).

This is the blocked version of the algorithm, calling Level 3 BLAS.```
Parameters
 [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.``` [in] N ``` N is INTEGER The order of the matrix A. N >= 0.``` [in,out] A ``` A is COMPLEX array, dimension (LDA,N) On entry, the hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, L is stored below (or above) the subdiagonal blocks, when UPLO is 'L' (or 'U').``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).``` [out] TB ``` TB is COMPLEX array, dimension (LTB) On exit, details of the LU factorization of the band matrix.``` [in] LTB ``` LTB is INTEGER The size of the array TB. LTB >= 4*N, internally used to select NB such that LTB >= (3*NB+1)*N. If LTB = -1, then a workspace query is assumed; the routine only calculates the optimal size of LTB, returns this value as the first entry of TB, and no error message related to LTB is issued by XERBLA.``` [out] IPIV ``` IPIV is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of A were interchanged with the row and column IPIV(k).``` [out] IPIV2 ``` IPIV2 is INTEGER array, dimension (N) On exit, it contains the details of the interchanges, i.e., the row and column k of T were interchanged with the row and column IPIV(k).``` [out] WORK ` WORK is COMPLEX workspace of size LWORK` [in] LWORK ``` LWORK is INTEGER The size of WORK. LWORK >= N, internally used to select NB such that LWORK >= N*NB. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.``` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = i, band LU factorization failed on i-th column```

Definition at line 158 of file csytrf_aa_2stage.f.

160*
161* -- LAPACK computational routine --
162* -- LAPACK is a software package provided by Univ. of Tennessee, --
163* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
164*
165 IMPLICIT NONE
166*
167* .. Scalar Arguments ..
168 CHARACTER UPLO
169 INTEGER N, LDA, LTB, LWORK, INFO
170* ..
171* .. Array Arguments ..
172 INTEGER IPIV( * ), IPIV2( * )
173 COMPLEX A( LDA, * ), TB( * ), WORK( * )
174* ..
175*
176* =====================================================================
177* .. Parameters ..
178 COMPLEX CZERO, CONE
179 parameter( czero = ( 0.0e+0, 0.0e+0 ),
180 \$ cone = ( 1.0e+0, 0.0e+0 ) )
181*
182* .. Local Scalars ..
183 LOGICAL UPPER, TQUERY, WQUERY
184 INTEGER I, J, K, I1, I2, TD
185 INTEGER LDTB, NB, KB, JB, NT, IINFO
186 COMPLEX PIV
187* ..
188* .. External Functions ..
189 LOGICAL LSAME
190 INTEGER ILAENV
191 REAL SROUNDUP_LWORK
192 EXTERNAL lsame, ilaenv, sroundup_lwork
193* ..
194* .. External Subroutines ..
195 EXTERNAL ccopy, cgbtrf, cgemm, cgetrf, clacpy,
197* ..
198* .. Intrinsic Functions ..
199 INTRINSIC min, max
200* ..
201* .. Executable Statements ..
202*
203* Test the input parameters.
204*
205 info = 0
206 upper = lsame( uplo, 'U' )
207 wquery = ( lwork.EQ.-1 )
208 tquery = ( ltb.EQ.-1 )
209 IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
210 info = -1
211 ELSE IF( n.LT.0 ) THEN
212 info = -2
213 ELSE IF( lda.LT.max( 1, n ) ) THEN
214 info = -4
215 ELSE IF ( ltb .LT. 4*n .AND. .NOT.tquery ) THEN
216 info = -6
217 ELSE IF ( lwork .LT. n .AND. .NOT.wquery ) THEN
218 info = -10
219 END IF
220*
221 IF( info.NE.0 ) THEN
222 CALL xerbla( 'CSYTRF_AA_2STAGE', -info )
223 RETURN
224 END IF
225*
227*
228 nb = ilaenv( 1, 'CSYTRF_AA_2STAGE', uplo, n, -1, -1, -1 )
229 IF( info.EQ.0 ) THEN
230 IF( tquery ) THEN
231 tb( 1 ) = (3*nb+1)*n
232 END IF
233 IF( wquery ) THEN
234 work( 1 ) = sroundup_lwork(n*nb)
235 END IF
236 END IF
237 IF( tquery .OR. wquery ) THEN
238 RETURN
239 END IF
240*
241* Quick return
242*
243 IF ( n.EQ.0 ) THEN
244 RETURN
245 ENDIF
246*
247* Determine the number of the block size
248*
249 ldtb = ltb/n
250 IF( ldtb .LT. 3*nb+1 ) THEN
251 nb = (ldtb-1)/3
252 END IF
253 IF( lwork .LT. nb*n ) THEN
254 nb = lwork/n
255 END IF
256*
257* Determine the number of the block columns
258*
259 nt = (n+nb-1)/nb
260 td = 2*nb
261 kb = min(nb, n)
262*
263* Initialize vectors/matrices
264*
265 DO j = 1, kb
266 ipiv( j ) = j
267 END DO
268*
269* Save NB
270*
271 tb( 1 ) = nb
272*
273 IF( upper ) THEN
274*
275* .....................................................
276* Factorize A as U**T*D*U using the upper triangle of A
277* .....................................................
278*
279 DO j = 0, nt-1
280*
281* Generate Jth column of W and H
282*
283 kb = min(nb, n-j*nb)
284 DO i = 1, j-1
285 IF( i.EQ.1 ) THEN
286* H(I,J) = T(I,I)*U(I,J) + T(I+1,I)*U(I+1,J)
287 IF( i .EQ. (j-1) ) THEN
288 jb = nb+kb
289 ELSE
290 jb = 2*nb
291 END IF
292 CALL cgemm( 'NoTranspose', 'NoTranspose',
293 \$ nb, kb, jb,
294 \$ cone, tb( td+1 + (i*nb)*ldtb ), ldtb-1,
295 \$ a( (i-1)*nb+1, j*nb+1 ), lda,
296 \$ czero, work( i*nb+1 ), n )
297 ELSE
298* H(I,J) = T(I,I-1)*U(I-1,J) + T(I,I)*U(I,J) + T(I,I+1)*U(I+1,J)
299 IF( i .EQ. j-1) THEN
300 jb = 2*nb+kb
301 ELSE
302 jb = 3*nb
303 END IF
304 CALL cgemm( 'NoTranspose', 'NoTranspose',
305 \$ nb, kb, jb,
306 \$ cone, tb( td+nb+1 + ((i-1)*nb)*ldtb ),
307 \$ ldtb-1,
308 \$ a( (i-2)*nb+1, j*nb+1 ), lda,
309 \$ czero, work( i*nb+1 ), n )
310 END IF
311 END DO
312*
313* Compute T(J,J)
314*
315 CALL clacpy( 'Upper', kb, kb, a( j*nb+1, j*nb+1 ), lda,
316 \$ tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
317 IF( j.GT.1 ) THEN
318* T(J,J) = U(1:J,J)'*H(1:J)
319 CALL cgemm( 'Transpose', 'NoTranspose',
320 \$ kb, kb, (j-1)*nb,
321 \$ -cone, a( 1, j*nb+1 ), lda,
322 \$ work( nb+1 ), n,
323 \$ cone, tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
324* T(J,J) += U(J,J)'*T(J,J-1)*U(J-1,J)
325 CALL cgemm( 'Transpose', 'NoTranspose',
326 \$ kb, nb, kb,
327 \$ cone, a( (j-1)*nb+1, j*nb+1 ), lda,
328 \$ tb( td+nb+1 + ((j-1)*nb)*ldtb ), ldtb-1,
329 \$ czero, work( 1 ), n )
330 CALL cgemm( 'NoTranspose', 'NoTranspose',
331 \$ kb, kb, nb,
332 \$ -cone, work( 1 ), n,
333 \$ a( (j-2)*nb+1, j*nb+1 ), lda,
334 \$ cone, tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
335 END IF
336*
337* Expand T(J,J) into full format
338*
339 DO i = 1, kb
340 DO k = i+1, kb
341 tb( td+(k-i)+1 + (j*nb+i-1)*ldtb )
342 \$ = tb( td-(k-(i+1)) + (j*nb+k-1)*ldtb )
343 END DO
344 END DO
345 IF( j.GT.0 ) THEN
346c CALL CHEGST( 1, 'Upper', KB,
347c \$ TB( TD+1 + (J*NB)*LDTB ), LDTB-1,
348c \$ A( (J-1)*NB+1, J*NB+1 ), LDA, IINFO )
349 CALL ctrsm( 'L', 'U', 'T', 'N', kb, kb, cone,
350 \$ a( (j-1)*nb+1, j*nb+1 ), lda,
351 \$ tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
352 CALL ctrsm( 'R', 'U', 'N', 'N', kb, kb, cone,
353 \$ a( (j-1)*nb+1, j*nb+1 ), lda,
354 \$ tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
355 END IF
356*
357 IF( j.LT.nt-1 ) THEN
358 IF( j.GT.0 ) THEN
359*
360* Compute H(J,J)
361*
362 IF( j.EQ.1 ) THEN
363 CALL cgemm( 'NoTranspose', 'NoTranspose',
364 \$ kb, kb, kb,
365 \$ cone, tb( td+1 + (j*nb)*ldtb ), ldtb-1,
366 \$ a( (j-1)*nb+1, j*nb+1 ), lda,
367 \$ czero, work( j*nb+1 ), n )
368 ELSE
369 CALL cgemm( 'NoTranspose', 'NoTranspose',
370 \$ kb, kb, nb+kb,
371 \$ cone, tb( td+nb+1 + ((j-1)*nb)*ldtb ),
372 \$ ldtb-1,
373 \$ a( (j-2)*nb+1, j*nb+1 ), lda,
374 \$ czero, work( j*nb+1 ), n )
375 END IF
376*
377* Update with the previous column
378*
379 CALL cgemm( 'Transpose', 'NoTranspose',
380 \$ nb, n-(j+1)*nb, j*nb,
381 \$ -cone, work( nb+1 ), n,
382 \$ a( 1, (j+1)*nb+1 ), lda,
383 \$ cone, a( j*nb+1, (j+1)*nb+1 ), lda )
384 END IF
385*
386* Copy panel to workspace to call CGETRF
387*
388 DO k = 1, nb
389 CALL ccopy( n-(j+1)*nb,
390 \$ a( j*nb+k, (j+1)*nb+1 ), lda,
391 \$ work( 1+(k-1)*n ), 1 )
392 END DO
393*
394* Factorize panel
395*
396 CALL cgetrf( n-(j+1)*nb, nb,
397 \$ work, n,
398 \$ ipiv( (j+1)*nb+1 ), iinfo )
399c IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN
400c INFO = IINFO+(J+1)*NB
401c END IF
402*
403* Copy panel back
404*
405 DO k = 1, nb
406 CALL ccopy( n-(j+1)*nb,
407 \$ work( 1+(k-1)*n ), 1,
408 \$ a( j*nb+k, (j+1)*nb+1 ), lda )
409 END DO
410*
411* Compute T(J+1, J), zero out for GEMM update
412*
413 kb = min(nb, n-(j+1)*nb)
414 CALL claset( 'Full', kb, nb, czero, czero,
415 \$ tb( td+nb+1 + (j*nb)*ldtb), ldtb-1 )
416 CALL clacpy( 'Upper', kb, nb,
417 \$ work, n,
418 \$ tb( td+nb+1 + (j*nb)*ldtb ), ldtb-1 )
419 IF( j.GT.0 ) THEN
420 CALL ctrsm( 'R', 'U', 'N', 'U', kb, nb, cone,
421 \$ a( (j-1)*nb+1, j*nb+1 ), lda,
422 \$ tb( td+nb+1 + (j*nb)*ldtb ), ldtb-1 )
423 END IF
424*
425* Copy T(J,J+1) into T(J+1, J), both upper/lower for GEMM
427*
428 DO k = 1, nb
429 DO i = 1, kb
430 tb( td-nb+k-i+1 + (j*nb+nb+i-1)*ldtb )
431 \$ = tb( td+nb+i-k+1 + (j*nb+k-1)*ldtb )
432 END DO
433 END DO
434 CALL claset( 'Lower', kb, nb, czero, cone,
435 \$ a( j*nb+1, (j+1)*nb+1), lda )
436*
437* Apply pivots to trailing submatrix of A
438*
439 DO k = 1, kb
441 ipiv( (j+1)*nb+k ) = ipiv( (j+1)*nb+k ) + (j+1)*nb
442*
443 i1 = (j+1)*nb+k
444 i2 = ipiv( (j+1)*nb+k )
445 IF( i1.NE.i2 ) THEN
446* > Apply pivots to previous columns of L
447 CALL cswap( k-1, a( (j+1)*nb+1, i1 ), 1,
448 \$ a( (j+1)*nb+1, i2 ), 1 )
449* > Swap A(I1+1:M, I1) with A(I2, I1+1:M)
450 IF( i2.GT.(i1+1) )
451 \$ CALL cswap( i2-i1-1, a( i1, i1+1 ), lda,
452 \$ a( i1+1, i2 ), 1 )
453* > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
454 IF( i2.LT.n )
455 \$ CALL cswap( n-i2, a( i1, i2+1 ), lda,
456 \$ a( i2, i2+1 ), lda )
457* > Swap A(I1, I1) with A(I2, I2)
458 piv = a( i1, i1 )
459 a( i1, i1 ) = a( i2, i2 )
460 a( i2, i2 ) = piv
461* > Apply pivots to previous columns of L
462 IF( j.GT.0 ) THEN
463 CALL cswap( j*nb, a( 1, i1 ), 1,
464 \$ a( 1, i2 ), 1 )
465 END IF
466 ENDIF
467 END DO
468 END IF
469 END DO
470 ELSE
471*
472* .....................................................
473* Factorize A as L*D*L**T using the lower triangle of A
474* .....................................................
475*
476 DO j = 0, nt-1
477*
478* Generate Jth column of W and H
479*
480 kb = min(nb, n-j*nb)
481 DO i = 1, j-1
482 IF( i.EQ.1 ) THEN
483* H(I,J) = T(I,I)*L(J,I)' + T(I+1,I)'*L(J,I+1)'
484 IF( i .EQ. (j-1) ) THEN
485 jb = nb+kb
486 ELSE
487 jb = 2*nb
488 END IF
489 CALL cgemm( 'NoTranspose', 'Transpose',
490 \$ nb, kb, jb,
491 \$ cone, tb( td+1 + (i*nb)*ldtb ), ldtb-1,
492 \$ a( j*nb+1, (i-1)*nb+1 ), lda,
493 \$ czero, work( i*nb+1 ), n )
494 ELSE
495* H(I,J) = T(I,I-1)*L(J,I-1)' + T(I,I)*L(J,I)' + T(I,I+1)*L(J,I+1)'
496 IF( i .EQ. (j-1) ) THEN
497 jb = 2*nb+kb
498 ELSE
499 jb = 3*nb
500 END IF
501 CALL cgemm( 'NoTranspose', 'Transpose',
502 \$ nb, kb, jb,
503 \$ cone, tb( td+nb+1 + ((i-1)*nb)*ldtb ),
504 \$ ldtb-1,
505 \$ a( j*nb+1, (i-2)*nb+1 ), lda,
506 \$ czero, work( i*nb+1 ), n )
507 END IF
508 END DO
509*
510* Compute T(J,J)
511*
512 CALL clacpy( 'Lower', kb, kb, a( j*nb+1, j*nb+1 ), lda,
513 \$ tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
514 IF( j.GT.1 ) THEN
515* T(J,J) = L(J,1:J)*H(1:J)
516 CALL cgemm( 'NoTranspose', 'NoTranspose',
517 \$ kb, kb, (j-1)*nb,
518 \$ -cone, a( j*nb+1, 1 ), lda,
519 \$ work( nb+1 ), n,
520 \$ cone, tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
521* T(J,J) += L(J,J)*T(J,J-1)*L(J,J-1)'
522 CALL cgemm( 'NoTranspose', 'NoTranspose',
523 \$ kb, nb, kb,
524 \$ cone, a( j*nb+1, (j-1)*nb+1 ), lda,
525 \$ tb( td+nb+1 + ((j-1)*nb)*ldtb ), ldtb-1,
526 \$ czero, work( 1 ), n )
527 CALL cgemm( 'NoTranspose', 'Transpose',
528 \$ kb, kb, nb,
529 \$ -cone, work( 1 ), n,
530 \$ a( j*nb+1, (j-2)*nb+1 ), lda,
531 \$ cone, tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
532 END IF
533*
534* Expand T(J,J) into full format
535*
536 DO i = 1, kb
537 DO k = i+1, kb
538 tb( td-(k-(i+1)) + (j*nb+k-1)*ldtb )
539 \$ = tb( td+(k-i)+1 + (j*nb+i-1)*ldtb )
540 END DO
541 END DO
542 IF( j.GT.0 ) THEN
543c CALL CHEGST( 1, 'Lower', KB,
544c \$ TB( TD+1 + (J*NB)*LDTB ), LDTB-1,
545c \$ A( J*NB+1, (J-1)*NB+1 ), LDA, IINFO )
546 CALL ctrsm( 'L', 'L', 'N', 'N', kb, kb, cone,
547 \$ a( j*nb+1, (j-1)*nb+1 ), lda,
548 \$ tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
549 CALL ctrsm( 'R', 'L', 'T', 'N', kb, kb, cone,
550 \$ a( j*nb+1, (j-1)*nb+1 ), lda,
551 \$ tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
552 END IF
553*
554* Symmetrize T(J,J)
555*
556 DO i = 1, kb
557 DO k = i+1, kb
558 tb( td-(k-(i+1)) + (j*nb+k-1)*ldtb )
559 \$ = tb( td+(k-i)+1 + (j*nb+i-1)*ldtb )
560 END DO
561 END DO
562*
563 IF( j.LT.nt-1 ) THEN
564 IF( j.GT.0 ) THEN
565*
566* Compute H(J,J)
567*
568 IF( j.EQ.1 ) THEN
569 CALL cgemm( 'NoTranspose', 'Transpose',
570 \$ kb, kb, kb,
571 \$ cone, tb( td+1 + (j*nb)*ldtb ), ldtb-1,
572 \$ a( j*nb+1, (j-1)*nb+1 ), lda,
573 \$ czero, work( j*nb+1 ), n )
574 ELSE
575 CALL cgemm( 'NoTranspose', 'Transpose',
576 \$ kb, kb, nb+kb,
577 \$ cone, tb( td+nb+1 + ((j-1)*nb)*ldtb ),
578 \$ ldtb-1,
579 \$ a( j*nb+1, (j-2)*nb+1 ), lda,
580 \$ czero, work( j*nb+1 ), n )
581 END IF
582*
583* Update with the previous column
584*
585 CALL cgemm( 'NoTranspose', 'NoTranspose',
586 \$ n-(j+1)*nb, nb, j*nb,
587 \$ -cone, a( (j+1)*nb+1, 1 ), lda,
588 \$ work( nb+1 ), n,
589 \$ cone, a( (j+1)*nb+1, j*nb+1 ), lda )
590 END IF
591*
592* Factorize panel
593*
594 CALL cgetrf( n-(j+1)*nb, nb,
595 \$ a( (j+1)*nb+1, j*nb+1 ), lda,
596 \$ ipiv( (j+1)*nb+1 ), iinfo )
597c IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN
598c INFO = IINFO+(J+1)*NB
599c END IF
600*
601* Compute T(J+1, J), zero out for GEMM update
602*
603 kb = min(nb, n-(j+1)*nb)
604 CALL claset( 'Full', kb, nb, czero, czero,
605 \$ tb( td+nb+1 + (j*nb)*ldtb), ldtb-1 )
606 CALL clacpy( 'Upper', kb, nb,
607 \$ a( (j+1)*nb+1, j*nb+1 ), lda,
608 \$ tb( td+nb+1 + (j*nb)*ldtb ), ldtb-1 )
609 IF( j.GT.0 ) THEN
610 CALL ctrsm( 'R', 'L', 'T', 'U', kb, nb, cone,
611 \$ a( j*nb+1, (j-1)*nb+1 ), lda,
612 \$ tb( td+nb+1 + (j*nb)*ldtb ), ldtb-1 )
613 END IF
614*
615* Copy T(J+1,J) into T(J, J+1), both upper/lower for GEMM
617*
618 DO k = 1, nb
619 DO i = 1, kb
620 tb( td-nb+k-i+1 + (j*nb+nb+i-1)*ldtb ) =
621 \$ tb( td+nb+i-k+1 + (j*nb+k-1)*ldtb )
622 END DO
623 END DO
624 CALL claset( 'Upper', kb, nb, czero, cone,
625 \$ a( (j+1)*nb+1, j*nb+1 ), lda )
626*
627* Apply pivots to trailing submatrix of A
628*
629 DO k = 1, kb
631 ipiv( (j+1)*nb+k ) = ipiv( (j+1)*nb+k ) + (j+1)*nb
632*
633 i1 = (j+1)*nb+k
634 i2 = ipiv( (j+1)*nb+k )
635 IF( i1.NE.i2 ) THEN
636* > Apply pivots to previous columns of L
637 CALL cswap( k-1, a( i1, (j+1)*nb+1 ), lda,
638 \$ a( i2, (j+1)*nb+1 ), lda )
639* > Swap A(I1+1:M, I1) with A(I2, I1+1:M)
640 IF( i2.GT.(i1+1) )
641 \$ CALL cswap( i2-i1-1, a( i1+1, i1 ), 1,
642 \$ a( i2, i1+1 ), lda )
643* > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
644 IF( i2.LT.n )
645 \$ CALL cswap( n-i2, a( i2+1, i1 ), 1,
646 \$ a( i2+1, i2 ), 1 )
647* > Swap A(I1, I1) with A(I2, I2)
648 piv = a( i1, i1 )
649 a( i1, i1 ) = a( i2, i2 )
650 a( i2, i2 ) = piv
651* > Apply pivots to previous columns of L
652 IF( j.GT.0 ) THEN
653 CALL cswap( j*nb, a( i1, 1 ), lda,
654 \$ a( i2, 1 ), lda )
655 END IF
656 ENDIF
657 END DO
658*
659* Apply pivots to previous columns of L
660*
661c CALL CLASWP( J*NB, A( 1, 1 ), LDA,
662c \$ (J+1)*NB+1, (J+1)*NB+KB, IPIV, 1 )
663 END IF
664 END DO
665 END IF
666*
667* Factor the band matrix
668 CALL cgbtrf( n, n, nb, nb, tb, ldtb, ipiv2, info )
669*
670 RETURN
671*
672* End of CSYTRF_AA_2STAGE
673*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine ccopy(n, cx, incx, cy, incy)
CCOPY
Definition ccopy.f:81
subroutine cgbtrf(m, n, kl, ku, ab, ldab, ipiv, info)
CGBTRF
Definition cgbtrf.f:144
subroutine cgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CGEMM
Definition cgemm.f:188
subroutine cgetrf(m, n, a, lda, ipiv, info)
CGETRF
Definition cgetrf.f:108
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
subroutine clacpy(uplo, m, n, a, lda, b, ldb)
CLACPY copies all or part of one two-dimensional array to another.
Definition clacpy.f:103
subroutine claset(uplo, m, n, alpha, beta, a, lda)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition claset.f:106
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
subroutine cswap(n, cx, incx, cy, incy)
CSWAP
Definition cswap.f:81
subroutine ctrsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
CTRSM
Definition ctrsm.f:180
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