LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ ssytrf_aa_2stage()

 subroutine ssytrf_aa_2stage ( character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tb, integer ltb, integer, dimension( * ) ipiv, integer, dimension( * ) ipiv2, real, dimension( * ) work, integer lwork, integer info )

SSYTRF_AA_2STAGE

Purpose:
``` SSYTRF_AA_2STAGE computes the factorization of a real 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 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 REAL array, dimension (LDA,N) On entry, the symmetric 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 REAL 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 REAL 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 ssytrf_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 REAL A( LDA, * ), TB( * ), WORK( * )
174* ..
175*
176* =====================================================================
177* .. Parameters ..
178 REAL ZERO, ONE
179 parameter( zero = 0.0e+0, one = 1.0e+0 )
180*
181* .. Local Scalars ..
182 LOGICAL UPPER, TQUERY, WQUERY
183 INTEGER I, J, K, I1, I2, TD
184 INTEGER LDTB, NB, KB, JB, NT, IINFO
185 REAL PIV
186* ..
187* .. External Functions ..
188 LOGICAL LSAME
189 INTEGER ILAENV
190 REAL SROUNDUP_LWORK
191 EXTERNAL lsame, ilaenv, sroundup_lwork
192* ..
193* .. External Subroutines ..
194 EXTERNAL xerbla, scopy, slacpy,
196 \$ ssygst, sswap, strsm
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( 'SSYTRF_AA_2STAGE', -info )
223 RETURN
224 END IF
225*
227*
228 nb = ilaenv( 1, 'SSYTRF_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 sgemm( 'NoTranspose', 'NoTranspose',
293 \$ nb, kb, jb,
294 \$ one, tb( td+1 + (i*nb)*ldtb ), ldtb-1,
295 \$ a( (i-1)*nb+1, j*nb+1 ), lda,
296 \$ zero, 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 sgemm( 'NoTranspose', 'NoTranspose',
305 \$ nb, kb, jb,
306 \$ one, tb( td+nb+1 + ((i-1)*nb)*ldtb ),
307 \$ ldtb-1,
308 \$ a( (i-2)*nb+1, j*nb+1 ), lda,
309 \$ zero, work( i*nb+1 ), n )
310 END IF
311 END DO
312*
313* Compute T(J,J)
314*
315 CALL slacpy( '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 sgemm( 'Transpose', 'NoTranspose',
320 \$ kb, kb, (j-1)*nb,
321 \$ -one, a( 1, j*nb+1 ), lda,
322 \$ work( nb+1 ), n,
323 \$ one, 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 sgemm( 'Transpose', 'NoTranspose',
326 \$ kb, nb, kb,
327 \$ one, a( (j-1)*nb+1, j*nb+1 ), lda,
328 \$ tb( td+nb+1 + ((j-1)*nb)*ldtb ), ldtb-1,
329 \$ zero, work( 1 ), n )
330 CALL sgemm( 'NoTranspose', 'NoTranspose',
331 \$ kb, kb, nb,
332 \$ -one, work( 1 ), n,
333 \$ a( (j-2)*nb+1, j*nb+1 ), lda,
334 \$ one, tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
335 END IF
336 IF( j.GT.0 ) THEN
337 CALL ssygst( 1, 'Upper', kb,
338 \$ tb( td+1 + (j*nb)*ldtb ), ldtb-1,
339 \$ a( (j-1)*nb+1, j*nb+1 ), lda, iinfo )
340 END IF
341*
342* Expand T(J,J) into full format
343*
344 DO i = 1, kb
345 DO k = i+1, kb
346 tb( td+(k-i)+1 + (j*nb+i-1)*ldtb )
347 \$ = tb( td-(k-(i+1)) + (j*nb+k-1)*ldtb )
348 END DO
349 END DO
350*
351 IF( j.LT.nt-1 ) THEN
352 IF( j.GT.0 ) THEN
353*
354* Compute H(J,J)
355*
356 IF( j.EQ.1 ) THEN
357 CALL sgemm( 'NoTranspose', 'NoTranspose',
358 \$ kb, kb, kb,
359 \$ one, tb( td+1 + (j*nb)*ldtb ), ldtb-1,
360 \$ a( (j-1)*nb+1, j*nb+1 ), lda,
361 \$ zero, work( j*nb+1 ), n )
362 ELSE
363 CALL sgemm( 'NoTranspose', 'NoTranspose',
364 \$ kb, kb, nb+kb,
365 \$ one, tb( td+nb+1 + ((j-1)*nb)*ldtb ),
366 \$ ldtb-1,
367 \$ a( (j-2)*nb+1, j*nb+1 ), lda,
368 \$ zero, work( j*nb+1 ), n )
369 END IF
370*
371* Update with the previous column
372*
373 CALL sgemm( 'Transpose', 'NoTranspose',
374 \$ nb, n-(j+1)*nb, j*nb,
375 \$ -one, work( nb+1 ), n,
376 \$ a( 1, (j+1)*nb+1 ), lda,
377 \$ one, a( j*nb+1, (j+1)*nb+1 ), lda )
378 END IF
379*
380* Copy panel to workspace to call SGETRF
381*
382 DO k = 1, nb
383 CALL scopy( n-(j+1)*nb,
384 \$ a( j*nb+k, (j+1)*nb+1 ), lda,
385 \$ work( 1+(k-1)*n ), 1 )
386 END DO
387*
388* Factorize panel
389*
390 CALL sgetrf( n-(j+1)*nb, nb,
391 \$ work, n,
392 \$ ipiv( (j+1)*nb+1 ), iinfo )
393c IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN
394c INFO = IINFO+(J+1)*NB
395c END IF
396*
397* Copy panel back
398*
399 DO k = 1, nb
400 CALL scopy( n-(j+1)*nb,
401 \$ work( 1+(k-1)*n ), 1,
402 \$ a( j*nb+k, (j+1)*nb+1 ), lda )
403 END DO
404*
405* Compute T(J+1, J), zero out for GEMM update
406*
407 kb = min(nb, n-(j+1)*nb)
408 CALL slaset( 'Full', kb, nb, zero, zero,
409 \$ tb( td+nb+1 + (j*nb)*ldtb), ldtb-1 )
410 CALL slacpy( 'Upper', kb, nb,
411 \$ work, n,
412 \$ tb( td+nb+1 + (j*nb)*ldtb ), ldtb-1 )
413 IF( j.GT.0 ) THEN
414 CALL strsm( 'R', 'U', 'N', 'U', kb, nb, one,
415 \$ a( (j-1)*nb+1, j*nb+1 ), lda,
416 \$ tb( td+nb+1 + (j*nb)*ldtb ), ldtb-1 )
417 END IF
418*
419* Copy T(J,J+1) into T(J+1, J), both upper/lower for GEMM
421*
422 DO k = 1, nb
423 DO i = 1, kb
424 tb( td-nb+k-i+1 + (j*nb+nb+i-1)*ldtb )
425 \$ = tb( td+nb+i-k+1 + (j*nb+k-1)*ldtb )
426 END DO
427 END DO
428 CALL slaset( 'Lower', kb, nb, zero, one,
429 \$ a( j*nb+1, (j+1)*nb+1), lda )
430*
431* Apply pivots to trailing submatrix of A
432*
433 DO k = 1, kb
435 ipiv( (j+1)*nb+k ) = ipiv( (j+1)*nb+k ) + (j+1)*nb
436*
437 i1 = (j+1)*nb+k
438 i2 = ipiv( (j+1)*nb+k )
439 IF( i1.NE.i2 ) THEN
440* > Apply pivots to previous columns of L
441 CALL sswap( k-1, a( (j+1)*nb+1, i1 ), 1,
442 \$ a( (j+1)*nb+1, i2 ), 1 )
443* > Swap A(I1+1:M, I1) with A(I2, I1+1:M)
444 IF( i2.GT.(i1+1) )
445 \$ CALL sswap( i2-i1-1, a( i1, i1+1 ), lda,
446 \$ a( i1+1, i2 ), 1 )
447* > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
448 IF( i2.LT.n )
449 \$ CALL sswap( n-i2, a( i1, i2+1 ), lda,
450 \$ a( i2, i2+1 ), lda )
451* > Swap A(I1, I1) with A(I2, I2)
452 piv = a( i1, i1 )
453 a( i1, i1 ) = a( i2, i2 )
454 a( i2, i2 ) = piv
455* > Apply pivots to previous columns of L
456 IF( j.GT.0 ) THEN
457 CALL sswap( j*nb, a( 1, i1 ), 1,
458 \$ a( 1, i2 ), 1 )
459 END IF
460 ENDIF
461 END DO
462 END IF
463 END DO
464 ELSE
465*
466* .....................................................
467* Factorize A as L*D*L**T using the lower triangle of A
468* .....................................................
469*
470 DO j = 0, nt-1
471*
472* Generate Jth column of W and H
473*
474 kb = min(nb, n-j*nb)
475 DO i = 1, j-1
476 IF( i.EQ.1 ) THEN
477* H(I,J) = T(I,I)*L(J,I)' + T(I+1,I)'*L(J,I+1)'
478 IF( i .EQ. (j-1) ) THEN
479 jb = nb+kb
480 ELSE
481 jb = 2*nb
482 END IF
483 CALL sgemm( 'NoTranspose', 'Transpose',
484 \$ nb, kb, jb,
485 \$ one, tb( td+1 + (i*nb)*ldtb ), ldtb-1,
486 \$ a( j*nb+1, (i-1)*nb+1 ), lda,
487 \$ zero, work( i*nb+1 ), n )
488 ELSE
489* 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)'
490 IF( i .EQ. j-1) THEN
491 jb = 2*nb+kb
492 ELSE
493 jb = 3*nb
494 END IF
495 CALL sgemm( 'NoTranspose', 'Transpose',
496 \$ nb, kb, jb,
497 \$ one, tb( td+nb+1 + ((i-1)*nb)*ldtb ),
498 \$ ldtb-1,
499 \$ a( j*nb+1, (i-2)*nb+1 ), lda,
500 \$ zero, work( i*nb+1 ), n )
501 END IF
502 END DO
503*
504* Compute T(J,J)
505*
506 CALL slacpy( 'Lower', kb, kb, a( j*nb+1, j*nb+1 ), lda,
507 \$ tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
508 IF( j.GT.1 ) THEN
509* T(J,J) = L(J,1:J)*H(1:J)
510 CALL sgemm( 'NoTranspose', 'NoTranspose',
511 \$ kb, kb, (j-1)*nb,
512 \$ -one, a( j*nb+1, 1 ), lda,
513 \$ work( nb+1 ), n,
514 \$ one, tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
515* T(J,J) += L(J,J)*T(J,J-1)*L(J,J-1)'
516 CALL sgemm( 'NoTranspose', 'NoTranspose',
517 \$ kb, nb, kb,
518 \$ one, a( j*nb+1, (j-1)*nb+1 ), lda,
519 \$ tb( td+nb+1 + ((j-1)*nb)*ldtb ), ldtb-1,
520 \$ zero, work( 1 ), n )
521 CALL sgemm( 'NoTranspose', 'Transpose',
522 \$ kb, kb, nb,
523 \$ -one, work( 1 ), n,
524 \$ a( j*nb+1, (j-2)*nb+1 ), lda,
525 \$ one, tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
526 END IF
527 IF( j.GT.0 ) THEN
528 CALL ssygst( 1, 'Lower', kb,
529 \$ tb( td+1 + (j*nb)*ldtb ), ldtb-1,
530 \$ a( j*nb+1, (j-1)*nb+1 ), lda, iinfo )
531 END IF
532*
533* Expand T(J,J) into full format
534*
535 DO i = 1, kb
536 DO k = i+1, kb
537 tb( td-(k-(i+1)) + (j*nb+k-1)*ldtb )
538 \$ = tb( td+(k-i)+1 + (j*nb+i-1)*ldtb )
539 END DO
540 END DO
541*
542 IF( j.LT.nt-1 ) THEN
543 IF( j.GT.0 ) THEN
544*
545* Compute H(J,J)
546*
547 IF( j.EQ.1 ) THEN
548 CALL sgemm( 'NoTranspose', 'Transpose',
549 \$ kb, kb, kb,
550 \$ one, tb( td+1 + (j*nb)*ldtb ), ldtb-1,
551 \$ a( j*nb+1, (j-1)*nb+1 ), lda,
552 \$ zero, work( j*nb+1 ), n )
553 ELSE
554 CALL sgemm( 'NoTranspose', 'Transpose',
555 \$ kb, kb, nb+kb,
556 \$ one, tb( td+nb+1 + ((j-1)*nb)*ldtb ),
557 \$ ldtb-1,
558 \$ a( j*nb+1, (j-2)*nb+1 ), lda,
559 \$ zero, work( j*nb+1 ), n )
560 END IF
561*
562* Update with the previous column
563*
564 CALL sgemm( 'NoTranspose', 'NoTranspose',
565 \$ n-(j+1)*nb, nb, j*nb,
566 \$ -one, a( (j+1)*nb+1, 1 ), lda,
567 \$ work( nb+1 ), n,
568 \$ one, a( (j+1)*nb+1, j*nb+1 ), lda )
569 END IF
570*
571* Factorize panel
572*
573 CALL sgetrf( n-(j+1)*nb, nb,
574 \$ a( (j+1)*nb+1, j*nb+1 ), lda,
575 \$ ipiv( (j+1)*nb+1 ), iinfo )
576c IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN
577c INFO = IINFO+(J+1)*NB
578c END IF
579*
580* Compute T(J+1, J), zero out for GEMM update
581*
582 kb = min(nb, n-(j+1)*nb)
583 CALL slaset( 'Full', kb, nb, zero, zero,
584 \$ tb( td+nb+1 + (j*nb)*ldtb), ldtb-1 )
585 CALL slacpy( 'Upper', kb, nb,
586 \$ a( (j+1)*nb+1, j*nb+1 ), lda,
587 \$ tb( td+nb+1 + (j*nb)*ldtb ), ldtb-1 )
588 IF( j.GT.0 ) THEN
589 CALL strsm( 'R', 'L', 'T', 'U', kb, nb, one,
590 \$ a( j*nb+1, (j-1)*nb+1 ), lda,
591 \$ tb( td+nb+1 + (j*nb)*ldtb ), ldtb-1 )
592 END IF
593*
594* Copy T(J+1,J) into T(J, J+1), both upper/lower for GEMM
596*
597 DO k = 1, nb
598 DO i = 1, kb
599 tb( td-nb+k-i+1 + (j*nb+nb+i-1)*ldtb ) =
600 \$ tb( td+nb+i-k+1 + (j*nb+k-1)*ldtb )
601 END DO
602 END DO
603 CALL slaset( 'Upper', kb, nb, zero, one,
604 \$ a( (j+1)*nb+1, j*nb+1), lda )
605*
606* Apply pivots to trailing submatrix of A
607*
608 DO k = 1, kb
610 ipiv( (j+1)*nb+k ) = ipiv( (j+1)*nb+k ) + (j+1)*nb
611*
612 i1 = (j+1)*nb+k
613 i2 = ipiv( (j+1)*nb+k )
614 IF( i1.NE.i2 ) THEN
615* > Apply pivots to previous columns of L
616 CALL sswap( k-1, a( i1, (j+1)*nb+1 ), lda,
617 \$ a( i2, (j+1)*nb+1 ), lda )
618* > Swap A(I1+1:M, I1) with A(I2, I1+1:M)
619 IF( i2.GT.(i1+1) )
620 \$ CALL sswap( i2-i1-1, a( i1+1, i1 ), 1,
621 \$ a( i2, i1+1 ), lda )
622* > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
623 IF( i2.LT.n )
624 \$ CALL sswap( n-i2, a( i2+1, i1 ), 1,
625 \$ a( i2+1, i2 ), 1 )
626* > Swap A(I1, I1) with A(I2, I2)
627 piv = a( i1, i1 )
628 a( i1, i1 ) = a( i2, i2 )
629 a( i2, i2 ) = piv
630* > Apply pivots to previous columns of L
631 IF( j.GT.0 ) THEN
632 CALL sswap( j*nb, a( i1, 1 ), lda,
633 \$ a( i2, 1 ), lda )
634 END IF
635 ENDIF
636 END DO
637*
638* Apply pivots to previous columns of L
639*
640c CALL SLASWP( J*NB, A( 1, 1 ), LDA,
641c \$ (J+1)*NB+1, (J+1)*NB+KB, IPIV, 1 )
642 END IF
643 END DO
644 END IF
645*
646* Factor the band matrix
647 CALL sgbtrf( n, n, nb, nb, tb, ldtb, ipiv2, info )
648*
649 RETURN
650*
651* End of SSYTRF_AA_2STAGE
652*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine scopy(n, sx, incx, sy, incy)
SCOPY
Definition scopy.f:82
subroutine sgbtrf(m, n, kl, ku, ab, ldab, ipiv, info)
SGBTRF
Definition sgbtrf.f:144
subroutine sgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
SGEMM
Definition sgemm.f:188
subroutine sgetrf(m, n, a, lda, ipiv, info)
SGETRF
Definition sgetrf.f:108
subroutine ssygst(itype, uplo, n, a, lda, b, ldb, info)
SSYGST
Definition ssygst.f:127
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
subroutine slacpy(uplo, m, n, a, lda, b, ldb)
SLACPY copies all or part of one two-dimensional array to another.
Definition slacpy.f:103
subroutine slaset(uplo, m, n, alpha, beta, a, lda)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition slaset.f:110
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
subroutine sswap(n, sx, incx, sy, incy)
SSWAP
Definition sswap.f:82
subroutine strsm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
STRSM
Definition strsm.f:181
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