LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ zheev_2stage()

subroutine zheev_2stage ( character jobz,
character uplo,
integer n,
complex*16, dimension( lda, * ) a,
integer lda,
double precision, dimension( * ) w,
complex*16, dimension( * ) work,
integer lwork,
double precision, dimension( * ) rwork,
integer info )

ZHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

Download ZHEEV_2STAGE + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> ZHEEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
!> complex Hermitian matrix A using the 2stage technique for
!> the reduction to tridiagonal.
!>
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 COMPLEX*16 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.  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 COMPLEX*16 array, dimension (MAX(1,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 = max(stage1,stage2) + (KD+1)*N + N
!>                                             = N*KD + N*max(KD+1,FACTOPTNB)
!>                                               + max(2*KD*KD, KD*NTHREADS)
!>                                               + (KD+1)*N + N
!>                                   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 queried. Not yet available
!>
!>          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]RWORK
!>          RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
!>
[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 185 of file zheev_2stage.f.

187*
188 IMPLICIT NONE
189*
190* -- LAPACK driver routine --
191* -- LAPACK is a software package provided by Univ. of Tennessee, --
192* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193*
194* .. Scalar Arguments ..
195 CHARACTER JOBZ, UPLO
196 INTEGER INFO, LDA, LWORK, N
197* ..
198* .. Array Arguments ..
199 DOUBLE PRECISION RWORK( * ), W( * )
200 COMPLEX*16 A( LDA, * ), WORK( * )
201* ..
202*
203* =====================================================================
204*
205* .. Parameters ..
206 DOUBLE PRECISION ZERO, ONE
207 parameter( zero = 0.0d0, one = 1.0d0 )
208 COMPLEX*16 CONE
209 parameter( cone = ( 1.0d0, 0.0d0 ) )
210* ..
211* .. Local Scalars ..
212 LOGICAL LOWER, LQUERY, WANTZ
213 INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
214 $ LLWORK, LWMIN, LHTRD, LWTRD, KD, IB, INDHOUS
215 DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
216 $ SMLNUM
217* ..
218* .. External Functions ..
219 LOGICAL LSAME
220 INTEGER ILAENV2STAGE
221 DOUBLE PRECISION DLAMCH, ZLANHE
222 EXTERNAL lsame, dlamch, zlanhe, ilaenv2stage
223* ..
224* .. External Subroutines ..
225 EXTERNAL dscal, dsterf, xerbla, zlascl,
226 $ zsteqr,
227 $ zungtr, zhetrd_2stage
228* ..
229* .. Intrinsic Functions ..
230 INTRINSIC dble, max, sqrt
231* ..
232* .. Executable Statements ..
233*
234* Test the input parameters.
235*
236 wantz = lsame( jobz, 'V' )
237 lower = lsame( uplo, 'L' )
238 lquery = ( lwork.EQ.-1 )
239*
240 info = 0
241 IF( .NOT.( lsame( jobz, 'N' ) ) ) THEN
242 info = -1
243 ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
244 info = -2
245 ELSE IF( n.LT.0 ) THEN
246 info = -3
247 ELSE IF( lda.LT.max( 1, n ) ) THEN
248 info = -5
249 END IF
250*
251 IF( info.EQ.0 ) THEN
252 kd = ilaenv2stage( 1, 'ZHETRD_2STAGE', jobz, n, -1, -1,
253 $ -1 )
254 ib = ilaenv2stage( 2, 'ZHETRD_2STAGE', jobz, n, kd, -1,
255 $ -1 )
256 lhtrd = ilaenv2stage( 3, 'ZHETRD_2STAGE', jobz, n, kd, ib,
257 $ -1 )
258 lwtrd = ilaenv2stage( 4, 'ZHETRD_2STAGE', jobz, n, kd, ib,
259 $ -1 )
260 lwmin = n + lhtrd + lwtrd
261 work( 1 ) = lwmin
262*
263 IF( lwork.LT.lwmin .AND. .NOT.lquery )
264 $ info = -8
265 END IF
266*
267 IF( info.NE.0 ) THEN
268 CALL xerbla( 'ZHEEV_2STAGE ', -info )
269 RETURN
270 ELSE IF( lquery ) THEN
271 RETURN
272 END IF
273*
274* Quick return if possible
275*
276 IF( n.EQ.0 ) THEN
277 RETURN
278 END IF
279*
280 IF( n.EQ.1 ) THEN
281 w( 1 ) = dble( a( 1, 1 ) )
282 work( 1 ) = 1
283 IF( wantz )
284 $ a( 1, 1 ) = cone
285 RETURN
286 END IF
287*
288* Get machine constants.
289*
290 safmin = dlamch( 'Safe minimum' )
291 eps = dlamch( 'Precision' )
292 smlnum = safmin / eps
293 bignum = one / smlnum
294 rmin = sqrt( smlnum )
295 rmax = sqrt( bignum )
296*
297* Scale matrix to allowable range, if necessary.
298*
299 anrm = zlanhe( 'M', uplo, n, a, lda, rwork )
300 iscale = 0
301 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
302 iscale = 1
303 sigma = rmin / anrm
304 ELSE IF( anrm.GT.rmax ) THEN
305 iscale = 1
306 sigma = rmax / anrm
307 END IF
308 IF( iscale.EQ.1 )
309 $ CALL zlascl( uplo, 0, 0, one, sigma, n, n, a, lda, info )
310*
311* Call ZHETRD_2STAGE to reduce Hermitian matrix to tridiagonal form.
312*
313 inde = 1
314 indtau = 1
315 indhous = indtau + n
316 indwrk = indhous + lhtrd
317 llwork = lwork - indwrk + 1
318*
319 CALL zhetrd_2stage( jobz, uplo, n, a, lda, w, rwork( inde ),
320 $ work( indtau ), work( indhous ), lhtrd,
321 $ work( indwrk ), llwork, iinfo )
322*
323* For eigenvalues only, call DSTERF. For eigenvectors, first call
324* ZUNGTR to generate the unitary matrix, then call ZSTEQR.
325*
326 IF( .NOT.wantz ) THEN
327 CALL dsterf( n, w, rwork( inde ), info )
328 ELSE
329 CALL zungtr( uplo, n, a, lda, work( indtau ),
330 $ work( indwrk ),
331 $ llwork, iinfo )
332 indwrk = inde + n
333 CALL zsteqr( jobz, n, w, rwork( inde ), a, lda,
334 $ rwork( indwrk ), info )
335 END IF
336*
337* If matrix was scaled, then rescale eigenvalues appropriately.
338*
339 IF( iscale.EQ.1 ) THEN
340 IF( info.EQ.0 ) THEN
341 imax = n
342 ELSE
343 imax = info - 1
344 END IF
345 CALL dscal( imax, one / sigma, w, 1 )
346 END IF
347*
348* Set WORK(1) to optimal complex workspace size.
349*
350 work( 1 ) = lwmin
351*
352 RETURN
353*
354* End of ZHEEV_2STAGE
355*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
zhetrd_2stage
subroutine zhetrd_2stage(vect, uplo, n, a, lda, d, e, tau, hous2, lhous2, work, lwork, info)
ZHETRD_2STAGE
Definition zhetrd_2stage.f:227
ilaenv2stage
integer function ilaenv2stage(ispec, name, opts, n1, n2, n3, n4)
ILAENV2STAGE
Definition ilaenv2stage.f:148
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
zlanhe
double precision function zlanhe(norm, uplo, n, a, lda, work)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition zlanhe.f:122
zlascl
subroutine zlascl(type, kl, ku, cfrom, cto, m, n, a, lda, info)
ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition zlascl.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
zsteqr
subroutine zsteqr(compz, n, d, e, z, ldz, work, info)
ZSTEQR
Definition zsteqr.f:130
dsterf
subroutine dsterf(n, d, e, info)
DSTERF
Definition dsterf.f:84
zungtr
subroutine zungtr(uplo, n, a, lda, tau, work, lwork, info)
ZUNGTR
Definition zungtr.f:121
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