LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ ssbevd_2stage()

subroutine ssbevd_2stage ( character jobz,
character uplo,
integer n,
integer kd,
real, dimension( ldab, * ) ab,
integer ldab,
real, dimension( * ) w,
real, dimension( ldz, * ) z,
integer ldz,
real, dimension( * ) work,
integer lwork,
integer, dimension( * ) iwork,
integer liwork,
integer info )

SSBEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Download SSBEVD_2STAGE + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> SSBEVD_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
!> a real symmetric band matrix A using the 2stage technique for
!> the reduction to tridiagonal. If eigenvectors are desired, it uses
!> a divide and conquer algorithm.
!>
!>
Parameters
[in]JOBZ
!>          JOBZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only;
!>          = 'V':  Compute eigenvalues and eigenvectors.
!>                  Not available in this release.
!>
[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]KD
!>          KD is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
!>
[in,out]AB
!>          AB is REAL array, dimension (LDAB, N)
!>          On entry, the upper or lower triangle of the symmetric band
!>          matrix A, stored in the first KD+1 rows of the array.  The
!>          j-th column of A is stored in the j-th column of the array AB
!>          as follows:
!>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>
!>          On exit, AB is overwritten by values generated during the
!>          reduction to tridiagonal form.  If UPLO = 'U', the first
!>          superdiagonal and the diagonal of the tridiagonal matrix T
!>          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
!>          the diagonal and first subdiagonal of T are returned in the
!>          first two rows of AB.
!>
[in]LDAB
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD + 1.
!>
[out]W
!>          W is REAL array, dimension (N)
!>          If INFO = 0, the eigenvalues in ascending order.
!>
[out]Z
!>          Z is REAL array, dimension (LDZ, N)
!>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
!>          eigenvectors of the matrix A, with the i-th column of Z
!>          holding the eigenvector associated with W(i).
!>          If JOBZ = 'N', then Z is not referenced.
!>
[in]LDZ
!>          LDZ is INTEGER
!>          The leading dimension of the array Z.  LDZ >= 1, and if
!>          JOBZ = 'V', LDZ >= max(1,N).
!>
[out]WORK
!>          WORK is REAL array, dimension LWORK
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>
[in]LWORK
!>          LWORK is INTEGER
!>          The length of the array WORK. LWORK >= 1, when N <= 1;
!>          otherwise
!>          If JOBZ = 'N' and N > 1, LWORK must be queried.
!>                                   LWORK = MAX(1, dimension) where
!>                                   dimension = (2KD+1)*N + KD*NTHREADS + N
!>                                   where KD is the size of the band.
!>                                   NTHREADS is the number of threads used when
!>                                   openMP compilation is enabled, otherwise =1.
!>          If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal sizes of the WORK and IWORK
!>          arrays, returns these values as the first entries of the WORK
!>          and IWORK arrays, and no error message related to LWORK or
!>          LIWORK is issued by XERBLA.
!>
[out]IWORK
!>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
!>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
!>
[in]LIWORK
!>          LIWORK is INTEGER
!>          The dimension of the array IWORK.
!>          If JOBZ  = 'N' or N <= 1, LIWORK must be at least 1.
!>          If JOBZ  = 'V' and N > 2, LIWORK must be at least 3 + 5*N.
!>
!>          If LIWORK = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal sizes of the WORK and
!>          IWORK arrays, returns these values as the first entries of
!>          the WORK and IWORK arrays, and no error message related to
!>          LWORK or LIWORK 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, the algorithm failed to converge; i
!>                off-diagonal elements of an intermediate tridiagonal
!>                form did not converge to zero.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!>
!>  All details about the 2stage techniques are available in:
!>
!>  Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
!>  Parallel reduction to condensed forms for symmetric eigenvalue problems
!>  using aggregated fine-grained and memory-aware kernels. In Proceedings
!>  of 2011 International Conference for High Performance Computing,
!>  Networking, Storage and Analysis (SC '11), New York, NY, USA,
!>  Article 8 , 11 pages.
!>  http://doi.acm.org/10.1145/2063384.2063394
!>
!>  A. Haidar, J. Kurzak, P. Luszczek, 2013.
!>  An improved parallel singular value algorithm and its implementation
!>  for multicore hardware, In Proceedings of 2013 International Conference
!>  for High Performance Computing, Networking, Storage and Analysis (SC '13).
!>  Denver, Colorado, USA, 2013.
!>  Article 90, 12 pages.
!>  http://doi.acm.org/10.1145/2503210.2503292
!>
!>  A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
!>  A novel hybrid CPU-GPU generalized eigensolver for electronic structure
!>  calculations based on fine-grained memory aware tasks.
!>  International Journal of High Performance Computing Applications.
!>  Volume 28 Issue 2, Pages 196-209, May 2014.
!>  http://hpc.sagepub.com/content/28/2/196
!>
!>

Definition at line 224 of file ssbevd_2stage.f.

227*
228 IMPLICIT NONE
229*
230* -- LAPACK driver routine --
231* -- LAPACK is a software package provided by Univ. of Tennessee, --
232* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
233*
234* .. Scalar Arguments ..
235 CHARACTER JOBZ, UPLO
236 INTEGER INFO, KD, LDAB, LDZ, LIWORK, LWORK, N
237* ..
238* .. Array Arguments ..
239 INTEGER IWORK( * )
240 REAL AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
241* ..
242*
243* =====================================================================
244*
245* .. Parameters ..
246 REAL ZERO, ONE
247 parameter( zero = 0.0e+0, one = 1.0e+0 )
248* ..
249* .. Local Scalars ..
250 LOGICAL LOWER, LQUERY, WANTZ
251 INTEGER IINFO, INDE, INDWK2, INDWRK, ISCALE, LIWMIN,
252 $ LLWORK, LWMIN, LHTRD, LWTRD, IB, INDHOUS,
253 $ LLWRK2
254 REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
255 $ SMLNUM
256* ..
257* .. External Functions ..
258 LOGICAL LSAME
259 INTEGER ILAENV2STAGE
260 REAL SLAMCH, SLANSB, SROUNDUP_LWORK
261 EXTERNAL lsame, slamch, slansb, ilaenv2stage,
262 $ sroundup_lwork
263* ..
264* .. External Subroutines ..
265 EXTERNAL sgemm, slacpy, slascl, sscal,
266 $ sstedc,
267 $ ssterf, xerbla, ssytrd_sb2st
268* ..
269* .. Intrinsic Functions ..
270 INTRINSIC sqrt
271* ..
272* .. Executable Statements ..
273*
274* Test the input parameters.
275*
276 wantz = lsame( jobz, 'V' )
277 lower = lsame( uplo, 'L' )
278 lquery = ( lwork.EQ.-1 .OR. liwork.EQ.-1 )
279*
280 info = 0
281 IF( n.LE.1 ) THEN
282 liwmin = 1
283 lwmin = 1
284 ELSE
285 ib = ilaenv2stage( 2, 'SSYTRD_SB2ST', jobz, n, kd, -1,
286 $ -1 )
287 lhtrd = ilaenv2stage( 3, 'SSYTRD_SB2ST', jobz, n, kd, ib,
288 $ -1 )
289 lwtrd = ilaenv2stage( 4, 'SSYTRD_SB2ST', jobz, n, kd, ib,
290 $ -1 )
291 IF( wantz ) THEN
292 liwmin = 3 + 5*n
293 lwmin = 1 + 5*n + 2*n**2
294 ELSE
295 liwmin = 1
296 lwmin = max( 2*n, n+lhtrd+lwtrd )
297 END IF
298 END IF
299 IF( .NOT.( lsame( jobz, 'N' ) ) ) THEN
300 info = -1
301 ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
302 info = -2
303 ELSE IF( n.LT.0 ) THEN
304 info = -3
305 ELSE IF( kd.LT.0 ) THEN
306 info = -4
307 ELSE IF( ldab.LT.kd+1 ) THEN
308 info = -6
309 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
310 info = -9
311 END IF
312*
313 IF( info.EQ.0 ) THEN
314 work( 1 ) = sroundup_lwork(lwmin)
315 iwork( 1 ) = liwmin
316*
317 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
318 info = -11
319 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
320 info = -13
321 END IF
322 END IF
323*
324 IF( info.NE.0 ) THEN
325 CALL xerbla( 'SSBEVD_2STAGE', -info )
326 RETURN
327 ELSE IF( lquery ) THEN
328 RETURN
329 END IF
330*
331* Quick return if possible
332*
333 IF( n.EQ.0 )
334 $ RETURN
335*
336 IF( n.EQ.1 ) THEN
337 w( 1 ) = ab( 1, 1 )
338 IF( wantz )
339 $ z( 1, 1 ) = one
340 RETURN
341 END IF
342*
343* Get machine constants.
344*
345 safmin = slamch( 'Safe minimum' )
346 eps = slamch( 'Precision' )
347 smlnum = safmin / eps
348 bignum = one / smlnum
349 rmin = sqrt( smlnum )
350 rmax = sqrt( bignum )
351*
352* Scale matrix to allowable range, if necessary.
353*
354 anrm = slansb( 'M', uplo, n, kd, ab, ldab, work )
355 iscale = 0
356 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
357 iscale = 1
358 sigma = rmin / anrm
359 ELSE IF( anrm.GT.rmax ) THEN
360 iscale = 1
361 sigma = rmax / anrm
362 END IF
363 IF( iscale.EQ.1 ) THEN
364 IF( lower ) THEN
365 CALL slascl( 'B', kd, kd, one, sigma, n, n, ab, ldab,
366 $ info )
367 ELSE
368 CALL slascl( 'Q', kd, kd, one, sigma, n, n, ab, ldab,
369 $ info )
370 END IF
371 END IF
372*
373* Call SSYTRD_SB2ST to reduce band symmetric matrix to tridiagonal form.
374*
375 inde = 1
376 indhous = inde + n
377 indwrk = indhous + lhtrd
378 llwork = lwork - indwrk + 1
379 indwk2 = indwrk + n*n
380 llwrk2 = lwork - indwk2 + 1
381*
382 CALL ssytrd_sb2st( "N", jobz, uplo, n, kd, ab, ldab, w,
383 $ work( inde ), work( indhous ), lhtrd,
384 $ work( indwrk ), llwork, iinfo )
385*
386* For eigenvalues only, call SSTERF. For eigenvectors, call SSTEDC.
387*
388 IF( .NOT.wantz ) THEN
389 CALL ssterf( n, w, work( inde ), info )
390 ELSE
391 CALL sstedc( 'I', n, w, work( inde ), work( indwrk ), n,
392 $ work( indwk2 ), llwrk2, iwork, liwork, info )
393 CALL sgemm( 'N', 'N', n, n, n, one, z, ldz, work( indwrk ),
394 $ n,
395 $ zero, work( indwk2 ), n )
396 CALL slacpy( 'A', n, n, work( indwk2 ), n, z, ldz )
397 END IF
398*
399* If matrix was scaled, then rescale eigenvalues appropriately.
400*
401 IF( iscale.EQ.1 )
402 $ CALL sscal( n, one / sigma, w, 1 )
403*
404 work( 1 ) = sroundup_lwork(lwmin)
405 iwork( 1 ) = liwmin
406 RETURN
407*
408* End of SSBEVD_2STAGE
409*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
sgemm
subroutine sgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
SGEMM
Definition sgemm.f:188
ssytrd_sb2st
subroutine ssytrd_sb2st(stage1, vect, uplo, n, kd, ab, ldab, d, e, hous, lhous, work, lwork, info)
SSYTRD_SB2ST reduces a real symmetric band matrix A to real symmetric tridiagonal form T
Definition ssytrd_sb2st.F:233
ilaenv2stage
integer function ilaenv2stage(ispec, name, opts, n1, n2, n3, n4)
ILAENV2STAGE
Definition ilaenv2stage.f:148
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:101
slamch
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
slansb
real function slansb(norm, uplo, n, k, ab, ldab, work)
SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition slansb.f:127
slascl
subroutine slascl(type, kl, ku, cfrom, cto, m, n, a, lda, info)
SLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition slascl.f:142
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
sroundup_lwork
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
Definition sroundup_lwork.f:59
sscal
subroutine sscal(n, sa, sx, incx)
SSCAL
Definition sscal.f:79
sstedc
subroutine sstedc(compz, n, d, e, z, ldz, work, lwork, iwork, liwork, info)
SSTEDC
Definition sstedc.f:180
ssterf
subroutine ssterf(n, d, e, info)
SSTERF
Definition ssterf.f:84
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