LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ dsygv_2stage()

subroutine dsygv_2stage ( integer  ITYPE,
character  JOBZ,
character  UPLO,
integer  N,
double precision, dimension( lda, * )  A,
integer  LDA,
double precision, dimension( ldb, * )  B,
integer  LDB,
double precision, dimension( * )  W,
double precision, dimension( * )  WORK,
integer  LWORK,
integer  INFO 
)

DSYGV_2STAGE

Download DSYGV_2STAGE + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 DSYGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
 of a real generalized symmetric-definite eigenproblem, of the form
 A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
 Here A and B are assumed to be symmetric and B is also
 positive definite.
 This routine use the 2stage technique for the reduction to tridiagonal
 which showed higher performance on recent architecture and for large
 sizes N>2000.
Parameters
[in]ITYPE
          ITYPE is INTEGER
          Specifies the problem type to be solved:
          = 1:  A*x = (lambda)*B*x
          = 2:  A*B*x = (lambda)*x
          = 3:  B*A*x = (lambda)*x
[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 triangles of A and B are stored;
          = 'L':  Lower triangles of A and B are stored.
[in]N
          N is INTEGER
          The order of the matrices A and B.  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
          matrix Z of eigenvectors.  The eigenvectors are normalized
          as follows:
          if ITYPE = 1 or 2, Z**T*B*Z = I;
          if ITYPE = 3, Z**T*inv(B)*Z = I.
          If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
          or the lower triangle (if UPLO='L') of A, including the
          diagonal, is destroyed.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[in,out]B
          B is DOUBLE PRECISION array, dimension (LDB, N)
          On entry, the symmetric positive definite matrix B.
          If UPLO = 'U', the leading N-by-N upper triangular part of B
          contains the upper triangular part of the matrix B.
          If UPLO = 'L', the leading N-by-N lower triangular part of B
          contains the lower triangular part of the matrix B.

          On exit, if INFO <= N, the part of B containing the matrix is
          overwritten by the triangular factor U or L from the Cholesky
          factorization B = U**T*U or B = L*L**T.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B.  LDB >= 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 (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 + 2*N
                                             = N*KD + N*max(KD+1,FACTOPTNB) 
                                               + max(2*KD*KD, KD*NTHREADS) 
                                               + (KD+1)*N + 2*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]INFO
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  DPOTRF or DSYEV returned an error code:
             <= N:  if INFO = i, DSYEV failed to converge;
                    i off-diagonal elements of an intermediate
                    tridiagonal form did not converge to zero;
             > N:   if INFO = N + i, for 1 <= i <= N, then the leading
                    minor of order i of B is not positive definite.
                    The factorization of B could not be completed and
                    no eigenvalues or eigenvectors were computed.
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 dsygv_2stage.f.

226*
227 IMPLICIT NONE
228*
229* -- LAPACK driver routine --
230* -- LAPACK is a software package provided by Univ. of Tennessee, --
231* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
232*
233* .. Scalar Arguments ..
234 CHARACTER JOBZ, UPLO
235 INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
236* ..
237* .. Array Arguments ..
238 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), W( * ), WORK( * )
239* ..
240*
241* =====================================================================
242*
243* .. Parameters ..
244 DOUBLE PRECISION ONE
245 parameter( one = 1.0d+0 )
246* ..
247* .. Local Scalars ..
248 LOGICAL LQUERY, UPPER, WANTZ
249 CHARACTER TRANS
250 INTEGER NEIG, LWMIN, LHTRD, LWTRD, KD, IB
251* ..
252* .. External Functions ..
253 LOGICAL LSAME
254 INTEGER ILAENV2STAGE
255 EXTERNAL lsame, ilaenv2stage
256* ..
257* .. External Subroutines ..
258 EXTERNAL dpotrf, dsygst, dtrmm, dtrsm, xerbla,
260* ..
261* .. Intrinsic Functions ..
262 INTRINSIC max
263* ..
264* .. Executable Statements ..
265*
266* Test the input parameters.
267*
268 wantz = lsame( jobz, 'V' )
269 upper = lsame( uplo, 'U' )
270 lquery = ( lwork.EQ.-1 )
271*
272 info = 0
273 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
274 info = -1
275 ELSE IF( .NOT.( lsame( jobz, 'N' ) ) ) THEN
276 info = -2
277 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
278 info = -3
279 ELSE IF( n.LT.0 ) THEN
280 info = -4
281 ELSE IF( lda.LT.max( 1, n ) ) THEN
282 info = -6
283 ELSE IF( ldb.LT.max( 1, n ) ) THEN
284 info = -8
285 END IF
286*
287 IF( info.EQ.0 ) THEN
288 kd = ilaenv2stage( 1, 'DSYTRD_2STAGE', jobz, n, -1, -1, -1 )
289 ib = ilaenv2stage( 2, 'DSYTRD_2STAGE', jobz, n, kd, -1, -1 )
290 lhtrd = ilaenv2stage( 3, 'DSYTRD_2STAGE', jobz, n, kd, ib, -1 )
291 lwtrd = ilaenv2stage( 4, 'DSYTRD_2STAGE', jobz, n, kd, ib, -1 )
292 lwmin = 2*n + lhtrd + lwtrd
293 work( 1 ) = lwmin
294*
295 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
296 info = -11
297 END IF
298 END IF
299*
300 IF( info.NE.0 ) THEN
301 CALL xerbla( 'DSYGV_2STAGE ', -info )
302 RETURN
303 ELSE IF( lquery ) THEN
304 RETURN
305 END IF
306*
307* Quick return if possible
308*
309 IF( n.EQ.0 )
310 $ RETURN
311*
312* Form a Cholesky factorization of B.
313*
314 CALL dpotrf( uplo, n, b, ldb, info )
315 IF( info.NE.0 ) THEN
316 info = n + info
317 RETURN
318 END IF
319*
320* Transform problem to standard eigenvalue problem and solve.
321*
322 CALL dsygst( itype, uplo, n, a, lda, b, ldb, info )
323 CALL dsyev_2stage( jobz, uplo, n, a, lda, w, work, lwork, info )
324*
325 IF( wantz ) THEN
326*
327* Backtransform eigenvectors to the original problem.
328*
329 neig = n
330 IF( info.GT.0 )
331 $ neig = info - 1
332 IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
333*
334* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
335* backtransform eigenvectors: x = inv(L)**T*y or inv(U)*y
336*
337 IF( upper ) THEN
338 trans = 'N'
339 ELSE
340 trans = 'T'
341 END IF
342*
343 CALL dtrsm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
344 $ b, ldb, a, lda )
345*
346 ELSE IF( itype.EQ.3 ) THEN
347*
348* For B*A*x=(lambda)*x;
349* backtransform eigenvectors: x = L*y or U**T*y
350*
351 IF( upper ) THEN
352 trans = 'T'
353 ELSE
354 trans = 'N'
355 END IF
356*
357 CALL dtrmm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
358 $ b, ldb, a, lda )
359 END IF
360 END IF
361*
362 work( 1 ) = lwmin
363 RETURN
364*
365* End of DSYGV_2STAGE
366*
integer function ilaenv2stage(ISPEC, NAME, OPTS, N1, N2, N3, N4)
ILAENV2STAGE
Definition: ilaenv2stage.f:149
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dtrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRSM
Definition: dtrsm.f:181
subroutine dtrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRMM
Definition: dtrmm.f:177
subroutine dpotrf(UPLO, N, A, LDA, INFO)
DPOTRF
Definition: dpotrf.f:107
subroutine dsygst(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
DSYGST
Definition: dsygst.f:127
subroutine dsyev_2stage(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, INFO)
DSYEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matr...
Definition: dsyev_2stage.f:183
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