LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dsyevd_2stage()

subroutine dsyevd_2stage ( character jobz,
character uplo,
integer n,
double precision, dimension( lda, * ) a,
integer lda,
double precision, dimension( * ) w,
double precision, dimension( * ) work,
integer lwork,
integer, dimension( * ) iwork,
integer liwork,
integer info )

DSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices

Download DSYEVD_2STAGE + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> DSYEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
!> real symmetric 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,out]A
!>          A is DOUBLE PRECISION 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.  If UPLO = 'L',
!>          the leading N-by-N lower triangular part of A contains
!>          the lower triangular part of the matrix A.
!>          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
!>          orthonormal eigenvectors of the matrix A.
!>          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
!>          or the upper triangle (if UPLO='U') of A, including the
!>          diagonal, is destroyed.
!>
[in]LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
[out]W
!>          W is DOUBLE PRECISION array, dimension (N)
!>          If INFO = 0, the eigenvalues in ascending order.
!>
[out]WORK
!>          WORK is DOUBLE PRECISION array,
!>                                         dimension (LWORK)
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>
[in]LWORK
!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>          If N <= 1,               LWORK must be at least 1.
!>          If JOBZ = 'N' and N > 1, LWORK must be queried.
!>                                   LWORK = MAX(1, dimension) where
!>                                   dimension = max(stage1,stage2) + (KD+1)*N + 2*N+1
!>                                             = N*KD + N*max(KD+1,FACTOPTNB)
!>                                               + max(2*KD*KD, KD*NTHREADS)
!>                                               + (KD+1)*N + 2*N+1
!>                                   where KD is the blocking size of the reduction,
!>                                   FACTOPTNB is the blocking used by the QR or LQ
!>                                   algorithm, usually FACTOPTNB=128 is a good choice
!>                                   NTHREADS is the number of threads used when
!>                                   openMP compilation is enabled, otherwise =1.
!>          If JOBZ = 'V' and N > 1, LWORK must be at least
!>                                                1 + 6*N + 2*N**2.
!>
!>          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 N <= 1,                LIWORK must be at least 1.
!>          If JOBZ  = 'N' and N > 1, LIWORK must be at least 1.
!>          If JOBZ  = 'V' and N > 1, 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 and JOBZ = 'N', then the algorithm failed
!>                to converge; i off-diagonal elements of an intermediate
!>                tridiagonal form did not converge to zero;
!>                if INFO = i and JOBZ = 'V', then the algorithm failed
!>                to compute an eigenvalue while working on the submatrix
!>                lying in rows and columns INFO/(N+1) through
!>                mod(INFO,N+1).
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
Modified by Francoise Tisseur, University of Tennessee
Modified description of INFO. Sven, 16 Feb 05.
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 217 of file dsyevd_2stage.f.

220*
221 IMPLICIT NONE
222*
223* -- LAPACK driver routine --
224* -- LAPACK is a software package provided by Univ. of Tennessee, --
225* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
226*
227* .. Scalar Arguments ..
228 CHARACTER JOBZ, UPLO
229 INTEGER INFO, LDA, LIWORK, LWORK, N
230* ..
231* .. Array Arguments ..
232 INTEGER IWORK( * )
233 DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
234* ..
235*
236* =====================================================================
237*
238* .. Parameters ..
239 DOUBLE PRECISION ZERO, ONE
240 parameter( zero = 0.0d+0, one = 1.0d+0 )
241* ..
242* .. Local Scalars ..
243*
244 LOGICAL LOWER, LQUERY, WANTZ
245 INTEGER IINFO, INDE, INDTAU, INDWK2, INDWRK, ISCALE,
246 $ LIWMIN, LLWORK, LLWRK2, LWMIN,
247 $ LHTRD, LWTRD, KD, IB, INDHOUS
248 DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
249 $ SMLNUM
250* ..
251* .. External Functions ..
252 LOGICAL LSAME
253 INTEGER ILAENV2STAGE
254 DOUBLE PRECISION DLAMCH, DLANSY
255 EXTERNAL lsame, dlamch, dlansy, ilaenv2stage
256* ..
257* .. External Subroutines ..
258 EXTERNAL dlacpy, dlascl, dormtr, dscal, dstedc,
259 $ dsterf,
260 $ dsytrd_2stage, xerbla
261* ..
262* .. Intrinsic Functions ..
263 INTRINSIC max, sqrt
264* ..
265* .. Executable Statements ..
266*
267* Test the input parameters.
268*
269 wantz = lsame( jobz, 'V' )
270 lower = lsame( uplo, 'L' )
271 lquery = ( lwork.EQ.-1 .OR. liwork.EQ.-1 )
272*
273 info = 0
274 IF( .NOT.( lsame( jobz, 'N' ) ) ) THEN
275 info = -1
276 ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
277 info = -2
278 ELSE IF( n.LT.0 ) THEN
279 info = -3
280 ELSE IF( lda.LT.max( 1, n ) ) THEN
281 info = -5
282 END IF
283*
284 IF( info.EQ.0 ) THEN
285 IF( n.LE.1 ) THEN
286 liwmin = 1
287 lwmin = 1
288 ELSE
289 kd = ilaenv2stage( 1, 'DSYTRD_2STAGE', jobz,
290 $ n, -1, -1, -1 )
291 ib = ilaenv2stage( 2, 'DSYTRD_2STAGE', jobz,
292 $ n, kd, -1, -1 )
293 lhtrd = ilaenv2stage( 3, 'DSYTRD_2STAGE', jobz,
294 $ n, kd, ib, -1 )
295 lwtrd = ilaenv2stage( 4, 'DSYTRD_2STAGE', jobz,
296 $ n, kd, ib, -1 )
297 IF( wantz ) THEN
298 liwmin = 3 + 5*n
299 lwmin = 1 + 6*n + 2*n**2
300 ELSE
301 liwmin = 1
302 lwmin = 2*n + 1 + lhtrd + lwtrd
303 END IF
304 END IF
305 work( 1 ) = lwmin
306 iwork( 1 ) = liwmin
307*
308 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
309 info = -8
310 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
311 info = -10
312 END IF
313 END IF
314*
315 IF( info.NE.0 ) THEN
316 CALL xerbla( 'DSYEVD_2STAGE', -info )
317 RETURN
318 ELSE IF( lquery ) THEN
319 RETURN
320 END IF
321*
322* Quick return if possible
323*
324 IF( n.EQ.0 )
325 $ RETURN
326*
327 IF( n.EQ.1 ) THEN
328 w( 1 ) = a( 1, 1 )
329 IF( wantz )
330 $ a( 1, 1 ) = one
331 RETURN
332 END IF
333*
334* Get machine constants.
335*
336 safmin = dlamch( 'Safe minimum' )
337 eps = dlamch( 'Precision' )
338 smlnum = safmin / eps
339 bignum = one / smlnum
340 rmin = sqrt( smlnum )
341 rmax = sqrt( bignum )
342*
343* Scale matrix to allowable range, if necessary.
344*
345 anrm = dlansy( 'M', uplo, n, a, lda, work )
346 iscale = 0
347 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
348 iscale = 1
349 sigma = rmin / anrm
350 ELSE IF( anrm.GT.rmax ) THEN
351 iscale = 1
352 sigma = rmax / anrm
353 END IF
354 IF( iscale.EQ.1 )
355 $ CALL dlascl( uplo, 0, 0, one, sigma, n, n, a, lda, info )
356*
357* Call DSYTRD_2STAGE to reduce symmetric matrix to tridiagonal form.
358*
359 inde = 1
360 indtau = inde + n
361 indhous = indtau + n
362 indwrk = indhous + lhtrd
363 llwork = lwork - indwrk + 1
364 indwk2 = indwrk + n*n
365 llwrk2 = lwork - indwk2 + 1
366*
367 CALL dsytrd_2stage( jobz, uplo, n, a, lda, w, work( inde ),
368 $ work( indtau ), work( indhous ), lhtrd,
369 $ work( indwrk ), llwork, iinfo )
370*
371* For eigenvalues only, call DSTERF. For eigenvectors, first call
372* DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
373* tridiagonal matrix, then call DORMTR to multiply it by the
374* Householder transformations stored in A.
375*
376 IF( .NOT.wantz ) THEN
377 CALL dsterf( n, w, work( inde ), info )
378 ELSE
379* Not available in this release, and argument checking should not
380* let it getting here
381 RETURN
382 CALL dstedc( 'I', n, w, work( inde ), work( indwrk ), n,
383 $ work( indwk2 ), llwrk2, iwork, liwork, info )
384 CALL dormtr( 'L', uplo, 'N', n, n, a, lda, work( indtau ),
385 $ work( indwrk ), n, work( indwk2 ), llwrk2, iinfo )
386 CALL dlacpy( 'A', n, n, work( indwrk ), n, a, lda )
387 END IF
388*
389* If matrix was scaled, then rescale eigenvalues appropriately.
390*
391 IF( iscale.EQ.1 )
392 $ CALL dscal( n, one / sigma, w, 1 )
393*
394 work( 1 ) = lwmin
395 iwork( 1 ) = liwmin
396*
397 RETURN
398*
399* End of DSYEVD_2STAGE
400*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dsytrd_2stage
subroutine dsytrd_2stage(vect, uplo, n, a, lda, d, e, tau, hous2, lhous2, work, lwork, info)
DSYTRD_2STAGE
Definition dsytrd_2stage.f:227
ilaenv2stage
integer function ilaenv2stage(ispec, name, opts, n1, n2, n3, n4)
ILAENV2STAGE
Definition ilaenv2stage.f:148
dlacpy
subroutine dlacpy(uplo, m, n, a, lda, b, ldb)
DLACPY copies all or part of one two-dimensional array to another.
Definition dlacpy.f:101
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
dlansy
double precision function dlansy(norm, uplo, n, a, lda, work)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition dlansy.f:120
dlascl
subroutine dlascl(type, kl, ku, cfrom, cto, m, n, a, lda, info)
DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition dlascl.f:142
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
dscal
subroutine dscal(n, da, dx, incx)
DSCAL
Definition dscal.f:79
dstedc
subroutine dstedc(compz, n, d, e, z, ldz, work, lwork, iwork, liwork, info)
DSTEDC
Definition dstedc.f:180
dsterf
subroutine dsterf(n, d, e, info)
DSTERF
Definition dsterf.f:84
dormtr
subroutine dormtr(side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info)
DORMTR
Definition dormtr.f:170
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