LAPACK  3.10.1
LAPACK: Linear Algebra PACKage

◆ 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

Download SSYTRF_AA_2STAGE + dependencies [TGZ] [ZIP] [TXT]

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 subdiaonal 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
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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  EXTERNAL lsame, ilaenv
191 * ..
192 * .. External Subroutines ..
193  EXTERNAL xerbla, scopy, slacpy,
194  $ slaset, sgbtrf, sgemm, sgetrf,
195  $ ssygst, sswap, strsm
196 * ..
197 * .. Intrinsic Functions ..
198  INTRINSIC min, max
199 * ..
200 * .. Executable Statements ..
201 *
202 * Test the input parameters.
203 *
204  info = 0
205  upper = lsame( uplo, 'U' )
206  wquery = ( lwork.EQ.-1 )
207  tquery = ( ltb.EQ.-1 )
208  IF( .NOT.upper .AND. .NOT.lsame( uplo, 'L' ) ) THEN
209  info = -1
210  ELSE IF( n.LT.0 ) THEN
211  info = -2
212  ELSE IF( lda.LT.max( 1, n ) ) THEN
213  info = -4
214  ELSE IF ( ltb .LT. 4*n .AND. .NOT.tquery ) THEN
215  info = -6
216  ELSE IF ( lwork .LT. n .AND. .NOT.wquery ) THEN
217  info = -10
218  END IF
219 *
220  IF( info.NE.0 ) THEN
221  CALL xerbla( 'SSYTRF_AA_2STAGE', -info )
222  RETURN
223  END IF
224 *
225 * Answer the query
226 *
227  nb = ilaenv( 1, 'SSYTRF_AA_2STAGE', uplo, n, -1, -1, -1 )
228  IF( info.EQ.0 ) THEN
229  IF( tquery ) THEN
230  tb( 1 ) = (3*nb+1)*n
231  END IF
232  IF( wquery ) THEN
233  work( 1 ) = n*nb
234  END IF
235  END IF
236  IF( tquery .OR. wquery ) THEN
237  RETURN
238  END IF
239 *
240 * Quick return
241 *
242  IF ( n.EQ.0 ) THEN
243  RETURN
244  ENDIF
245 *
246 * Determine the number of the block size
247 *
248  ldtb = ltb/n
249  IF( ldtb .LT. 3*nb+1 ) THEN
250  nb = (ldtb-1)/3
251  END IF
252  IF( lwork .LT. nb*n ) THEN
253  nb = lwork/n
254  END IF
255 *
256 * Determine the number of the block columns
257 *
258  nt = (n+nb-1)/nb
259  td = 2*nb
260  kb = min(nb, n)
261 *
262 * Initialize vectors/matrices
263 *
264  DO j = 1, kb
265  ipiv( j ) = j
266  END DO
267 *
268 * Save NB
269 *
270  tb( 1 ) = nb
271 *
272  IF( upper ) THEN
273 *
274 * .....................................................
275 * Factorize A as U**T*D*U using the upper triangle of A
276 * .....................................................
277 *
278  DO j = 0, nt-1
279 *
280 * Generate Jth column of W and H
281 *
282  kb = min(nb, n-j*nb)
283  DO i = 1, j-1
284  IF( i.EQ.1 ) THEN
285 * H(I,J) = T(I,I)*U(I,J) + T(I+1,I)*U(I+1,J)
286  IF( i .EQ. (j-1) ) THEN
287  jb = nb+kb
288  ELSE
289  jb = 2*nb
290  END IF
291  CALL sgemm( 'NoTranspose', 'NoTranspose',
292  $ nb, kb, jb,
293  $ one, tb( td+1 + (i*nb)*ldtb ), ldtb-1,
294  $ a( (i-1)*nb+1, j*nb+1 ), lda,
295  $ zero, work( i*nb+1 ), n )
296  ELSE
297 * 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)
298  IF( i .EQ. j-1) THEN
299  jb = 2*nb+kb
300  ELSE
301  jb = 3*nb
302  END IF
303  CALL sgemm( 'NoTranspose', 'NoTranspose',
304  $ nb, kb, jb,
305  $ one, tb( td+nb+1 + ((i-1)*nb)*ldtb ),
306  $ ldtb-1,
307  $ a( (i-2)*nb+1, j*nb+1 ), lda,
308  $ zero, work( i*nb+1 ), n )
309  END IF
310  END DO
311 *
312 * Compute T(J,J)
313 *
314  CALL slacpy( 'Upper', kb, kb, a( j*nb+1, j*nb+1 ), lda,
315  $ tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
316  IF( j.GT.1 ) THEN
317 * T(J,J) = U(1:J,J)'*H(1:J)
318  CALL sgemm( 'Transpose', 'NoTranspose',
319  $ kb, kb, (j-1)*nb,
320  $ -one, a( 1, j*nb+1 ), lda,
321  $ work( nb+1 ), n,
322  $ one, tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
323 * T(J,J) += U(J,J)'*T(J,J-1)*U(J-1,J)
324  CALL sgemm( 'Transpose', 'NoTranspose',
325  $ kb, nb, kb,
326  $ one, a( (j-1)*nb+1, j*nb+1 ), lda,
327  $ tb( td+nb+1 + ((j-1)*nb)*ldtb ), ldtb-1,
328  $ zero, work( 1 ), n )
329  CALL sgemm( 'NoTranspose', 'NoTranspose',
330  $ kb, kb, nb,
331  $ -one, work( 1 ), n,
332  $ a( (j-2)*nb+1, j*nb+1 ), lda,
333  $ one, tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
334  END IF
335  IF( j.GT.0 ) THEN
336  CALL ssygst( 1, 'Upper', kb,
337  $ tb( td+1 + (j*nb)*ldtb ), ldtb-1,
338  $ a( (j-1)*nb+1, j*nb+1 ), lda, iinfo )
339  END IF
340 *
341 * Expand T(J,J) into full format
342 *
343  DO i = 1, kb
344  DO k = i+1, kb
345  tb( td+(k-i)+1 + (j*nb+i-1)*ldtb )
346  $ = tb( td-(k-(i+1)) + (j*nb+k-1)*ldtb )
347  END DO
348  END DO
349 *
350  IF( j.LT.nt-1 ) THEN
351  IF( j.GT.0 ) THEN
352 *
353 * Compute H(J,J)
354 *
355  IF( j.EQ.1 ) THEN
356  CALL sgemm( 'NoTranspose', 'NoTranspose',
357  $ kb, kb, kb,
358  $ one, tb( td+1 + (j*nb)*ldtb ), ldtb-1,
359  $ a( (j-1)*nb+1, j*nb+1 ), lda,
360  $ zero, work( j*nb+1 ), n )
361  ELSE
362  CALL sgemm( 'NoTranspose', 'NoTranspose',
363  $ kb, kb, nb+kb,
364  $ one, tb( td+nb+1 + ((j-1)*nb)*ldtb ),
365  $ ldtb-1,
366  $ a( (j-2)*nb+1, j*nb+1 ), lda,
367  $ zero, work( j*nb+1 ), n )
368  END IF
369 *
370 * Update with the previous column
371 *
372  CALL sgemm( 'Transpose', 'NoTranspose',
373  $ nb, n-(j+1)*nb, j*nb,
374  $ -one, work( nb+1 ), n,
375  $ a( 1, (j+1)*nb+1 ), lda,
376  $ one, a( j*nb+1, (j+1)*nb+1 ), lda )
377  END IF
378 *
379 * Copy panel to workspace to call SGETRF
380 *
381  DO k = 1, nb
382  CALL scopy( n-(j+1)*nb,
383  $ a( j*nb+k, (j+1)*nb+1 ), lda,
384  $ work( 1+(k-1)*n ), 1 )
385  END DO
386 *
387 * Factorize panel
388 *
389  CALL sgetrf( n-(j+1)*nb, nb,
390  $ work, n,
391  $ ipiv( (j+1)*nb+1 ), iinfo )
392 c IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN
393 c INFO = IINFO+(J+1)*NB
394 c END IF
395 *
396 * Copy panel back
397 *
398  DO k = 1, nb
399  CALL scopy( n-(j+1)*nb,
400  $ work( 1+(k-1)*n ), 1,
401  $ a( j*nb+k, (j+1)*nb+1 ), lda )
402  END DO
403 *
404 * Compute T(J+1, J), zero out for GEMM update
405 *
406  kb = min(nb, n-(j+1)*nb)
407  CALL slaset( 'Full', kb, nb, zero, zero,
408  $ tb( td+nb+1 + (j*nb)*ldtb), ldtb-1 )
409  CALL slacpy( 'Upper', kb, nb,
410  $ work, n,
411  $ tb( td+nb+1 + (j*nb)*ldtb ), ldtb-1 )
412  IF( j.GT.0 ) THEN
413  CALL strsm( 'R', 'U', 'N', 'U', kb, nb, one,
414  $ a( (j-1)*nb+1, j*nb+1 ), lda,
415  $ tb( td+nb+1 + (j*nb)*ldtb ), ldtb-1 )
416  END IF
417 *
418 * Copy T(J,J+1) into T(J+1, J), both upper/lower for GEMM
419 * updates
420 *
421  DO k = 1, nb
422  DO i = 1, kb
423  tb( td-nb+k-i+1 + (j*nb+nb+i-1)*ldtb )
424  $ = tb( td+nb+i-k+1 + (j*nb+k-1)*ldtb )
425  END DO
426  END DO
427  CALL slaset( 'Lower', kb, nb, zero, one,
428  $ a( j*nb+1, (j+1)*nb+1), lda )
429 *
430 * Apply pivots to trailing submatrix of A
431 *
432  DO k = 1, kb
433 * > Adjust ipiv
434  ipiv( (j+1)*nb+k ) = ipiv( (j+1)*nb+k ) + (j+1)*nb
435 *
436  i1 = (j+1)*nb+k
437  i2 = ipiv( (j+1)*nb+k )
438  IF( i1.NE.i2 ) THEN
439 * > Apply pivots to previous columns of L
440  CALL sswap( k-1, a( (j+1)*nb+1, i1 ), 1,
441  $ a( (j+1)*nb+1, i2 ), 1 )
442 * > Swap A(I1+1:M, I1) with A(I2, I1+1:M)
443  IF( i2.GT.(i1+1) )
444  $ CALL sswap( i2-i1-1, a( i1, i1+1 ), lda,
445  $ a( i1+1, i2 ), 1 )
446 * > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
447  IF( i2.LT.n )
448  $ CALL sswap( n-i2, a( i1, i2+1 ), lda,
449  $ a( i2, i2+1 ), lda )
450 * > Swap A(I1, I1) with A(I2, I2)
451  piv = a( i1, i1 )
452  a( i1, i1 ) = a( i2, i2 )
453  a( i2, i2 ) = piv
454 * > Apply pivots to previous columns of L
455  IF( j.GT.0 ) THEN
456  CALL sswap( j*nb, a( 1, i1 ), 1,
457  $ a( 1, i2 ), 1 )
458  END IF
459  ENDIF
460  END DO
461  END IF
462  END DO
463  ELSE
464 *
465 * .....................................................
466 * Factorize A as L*D*L**T using the lower triangle of A
467 * .....................................................
468 *
469  DO j = 0, nt-1
470 *
471 * Generate Jth column of W and H
472 *
473  kb = min(nb, n-j*nb)
474  DO i = 1, j-1
475  IF( i.EQ.1 ) THEN
476 * H(I,J) = T(I,I)*L(J,I)' + T(I+1,I)'*L(J,I+1)'
477  IF( i .EQ. (j-1) ) THEN
478  jb = nb+kb
479  ELSE
480  jb = 2*nb
481  END IF
482  CALL sgemm( 'NoTranspose', 'Transpose',
483  $ nb, kb, jb,
484  $ one, tb( td+1 + (i*nb)*ldtb ), ldtb-1,
485  $ a( j*nb+1, (i-1)*nb+1 ), lda,
486  $ zero, work( i*nb+1 ), n )
487  ELSE
488 * 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)'
489  IF( i .EQ. j-1) THEN
490  jb = 2*nb+kb
491  ELSE
492  jb = 3*nb
493  END IF
494  CALL sgemm( 'NoTranspose', 'Transpose',
495  $ nb, kb, jb,
496  $ one, tb( td+nb+1 + ((i-1)*nb)*ldtb ),
497  $ ldtb-1,
498  $ a( j*nb+1, (i-2)*nb+1 ), lda,
499  $ zero, work( i*nb+1 ), n )
500  END IF
501  END DO
502 *
503 * Compute T(J,J)
504 *
505  CALL slacpy( 'Lower', kb, kb, a( j*nb+1, j*nb+1 ), lda,
506  $ tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
507  IF( j.GT.1 ) THEN
508 * T(J,J) = L(J,1:J)*H(1:J)
509  CALL sgemm( 'NoTranspose', 'NoTranspose',
510  $ kb, kb, (j-1)*nb,
511  $ -one, a( j*nb+1, 1 ), lda,
512  $ work( nb+1 ), n,
513  $ one, tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
514 * T(J,J) += L(J,J)*T(J,J-1)*L(J,J-1)'
515  CALL sgemm( 'NoTranspose', 'NoTranspose',
516  $ kb, nb, kb,
517  $ one, a( j*nb+1, (j-1)*nb+1 ), lda,
518  $ tb( td+nb+1 + ((j-1)*nb)*ldtb ), ldtb-1,
519  $ zero, work( 1 ), n )
520  CALL sgemm( 'NoTranspose', 'Transpose',
521  $ kb, kb, nb,
522  $ -one, work( 1 ), n,
523  $ a( j*nb+1, (j-2)*nb+1 ), lda,
524  $ one, tb( td+1 + (j*nb)*ldtb ), ldtb-1 )
525  END IF
526  IF( j.GT.0 ) THEN
527  CALL ssygst( 1, 'Lower', kb,
528  $ tb( td+1 + (j*nb)*ldtb ), ldtb-1,
529  $ a( j*nb+1, (j-1)*nb+1 ), lda, iinfo )
530  END IF
531 *
532 * Expand T(J,J) into full format
533 *
534  DO i = 1, kb
535  DO k = i+1, kb
536  tb( td-(k-(i+1)) + (j*nb+k-1)*ldtb )
537  $ = tb( td+(k-i)+1 + (j*nb+i-1)*ldtb )
538  END DO
539  END DO
540 *
541  IF( j.LT.nt-1 ) THEN
542  IF( j.GT.0 ) THEN
543 *
544 * Compute H(J,J)
545 *
546  IF( j.EQ.1 ) THEN
547  CALL sgemm( 'NoTranspose', 'Transpose',
548  $ kb, kb, kb,
549  $ one, tb( td+1 + (j*nb)*ldtb ), ldtb-1,
550  $ a( j*nb+1, (j-1)*nb+1 ), lda,
551  $ zero, work( j*nb+1 ), n )
552  ELSE
553  CALL sgemm( 'NoTranspose', 'Transpose',
554  $ kb, kb, nb+kb,
555  $ one, tb( td+nb+1 + ((j-1)*nb)*ldtb ),
556  $ ldtb-1,
557  $ a( j*nb+1, (j-2)*nb+1 ), lda,
558  $ zero, work( j*nb+1 ), n )
559  END IF
560 *
561 * Update with the previous column
562 *
563  CALL sgemm( 'NoTranspose', 'NoTranspose',
564  $ n-(j+1)*nb, nb, j*nb,
565  $ -one, a( (j+1)*nb+1, 1 ), lda,
566  $ work( nb+1 ), n,
567  $ one, a( (j+1)*nb+1, j*nb+1 ), lda )
568  END IF
569 *
570 * Factorize panel
571 *
572  CALL sgetrf( n-(j+1)*nb, nb,
573  $ a( (j+1)*nb+1, j*nb+1 ), lda,
574  $ ipiv( (j+1)*nb+1 ), iinfo )
575 c IF (IINFO.NE.0 .AND. INFO.EQ.0) THEN
576 c INFO = IINFO+(J+1)*NB
577 c END IF
578 *
579 * Compute T(J+1, J), zero out for GEMM update
580 *
581  kb = min(nb, n-(j+1)*nb)
582  CALL slaset( 'Full', kb, nb, zero, zero,
583  $ tb( td+nb+1 + (j*nb)*ldtb), ldtb-1 )
584  CALL slacpy( 'Upper', kb, nb,
585  $ a( (j+1)*nb+1, j*nb+1 ), lda,
586  $ tb( td+nb+1 + (j*nb)*ldtb ), ldtb-1 )
587  IF( j.GT.0 ) THEN
588  CALL strsm( 'R', 'L', 'T', 'U', kb, nb, one,
589  $ a( j*nb+1, (j-1)*nb+1 ), lda,
590  $ tb( td+nb+1 + (j*nb)*ldtb ), ldtb-1 )
591  END IF
592 *
593 * Copy T(J+1,J) into T(J, J+1), both upper/lower for GEMM
594 * updates
595 *
596  DO k = 1, nb
597  DO i = 1, kb
598  tb( td-nb+k-i+1 + (j*nb+nb+i-1)*ldtb ) =
599  $ tb( td+nb+i-k+1 + (j*nb+k-1)*ldtb )
600  END DO
601  END DO
602  CALL slaset( 'Upper', kb, nb, zero, one,
603  $ a( (j+1)*nb+1, j*nb+1), lda )
604 *
605 * Apply pivots to trailing submatrix of A
606 *
607  DO k = 1, kb
608 * > Adjust ipiv
609  ipiv( (j+1)*nb+k ) = ipiv( (j+1)*nb+k ) + (j+1)*nb
610 *
611  i1 = (j+1)*nb+k
612  i2 = ipiv( (j+1)*nb+k )
613  IF( i1.NE.i2 ) THEN
614 * > Apply pivots to previous columns of L
615  CALL sswap( k-1, a( i1, (j+1)*nb+1 ), lda,
616  $ a( i2, (j+1)*nb+1 ), lda )
617 * > Swap A(I1+1:M, I1) with A(I2, I1+1:M)
618  IF( i2.GT.(i1+1) )
619  $ CALL sswap( i2-i1-1, a( i1+1, i1 ), 1,
620  $ a( i2, i1+1 ), lda )
621 * > Swap A(I2+1:M, I1) with A(I2+1:M, I2)
622  IF( i2.LT.n )
623  $ CALL sswap( n-i2, a( i2+1, i1 ), 1,
624  $ a( i2+1, i2 ), 1 )
625 * > Swap A(I1, I1) with A(I2, I2)
626  piv = a( i1, i1 )
627  a( i1, i1 ) = a( i2, i2 )
628  a( i2, i2 ) = piv
629 * > Apply pivots to previous columns of L
630  IF( j.GT.0 ) THEN
631  CALL sswap( j*nb, a( i1, 1 ), lda,
632  $ a( i2, 1 ), lda )
633  END IF
634  ENDIF
635  END DO
636 *
637 * Apply pivots to previous columns of L
638 *
639 c CALL SLASWP( J*NB, A( 1, 1 ), LDA,
640 c $ (J+1)*NB+1, (J+1)*NB+KB, IPIV, 1 )
641  END IF
642  END DO
643  END IF
644 *
645 * Factor the band matrix
646  CALL sgbtrf( n, n, nb, nb, tb, ldtb, ipiv2, info )
647 *
648  RETURN
649 *
650 * End of SSYTRF_AA_2STAGE
651 *
slaset
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
slacpy
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
ilaenv
integer function ilaenv(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV
Definition: ilaenv.f:162
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
sgbtrf
subroutine sgbtrf(M, N, KL, KU, AB, LDAB, IPIV, INFO)
SGBTRF
Definition: sgbtrf.f:144
sgetrf
subroutine sgetrf(M, N, A, LDA, IPIV, INFO)
SGETRF
Definition: sgetrf.f:108
ssygst
subroutine ssygst(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
SSYGST
Definition: ssygst.f:127
sswap
subroutine sswap(N, SX, INCX, SY, INCY)
SSWAP
Definition: sswap.f:82
scopy
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
strsm
subroutine strsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRSM
Definition: strsm.f:181
sgemm
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187
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